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searching for Structure (mathematical logic) 392 found (608 total)

alternate case: structure (mathematical logic)

Turnstile (symbol) (1,171 words) [view diff] no match in snippet view article

In mathematical logic and computer science the symbol ⊢ ( ⊢ {\displaystyle \vdash } ) has taken the name turnstile because of its resemblance to a typical

Double turnstile (460 words) [view diff] no match in snippet view article find links to article

satisfaction, with a model (or truth-structure) on the left and a set of sentences on the right, to denote that the structure is a model for (or satisfies) the

Successor function (389 words) [view diff] no match in snippet view article find links to article

the formal language used to state the Peano axioms, which formalise the structure of the natural numbers. In this formalisation, the successor function

Algebraic theory (432 words) [view diff] no match in snippet view article find links to article

Informally in mathematical logic, an algebraic theory is a theory that uses axioms stated entirely in terms of equations between terms with free variables

Top type (992 words) [view diff] no match in snippet view article find links to article

In mathematical logic and computer science, some type theories and type systems include a top type that is commonly denoted with top or the symbol ⊤. The

Cointerpretability (191 words) [view diff] no match in snippet view article find links to article

In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory T is cointerpretable in another such theory S, when

Metamathematics (1,666 words) [view diff] no match in snippet view article find links to article

themselves contain itself?). Metamathematics was intimately connected to mathematical logic, so that the early histories of the two fields, during the late 19th

Term algebra (2,175 words) [view diff] no match in snippet view article find links to article

In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature

Descriptive set theory (1,590 words) [view diff] no match in snippet view article find links to article

In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces

Indeterminacy in concurrent computation (1,318 words) [view diff] no match in snippet view article find links to article

they cannot be deduced from prior information by mathematical logic alone. Therefore, mathematical logic cannot implement concurrent computation in open

Ronald Jensen (625 words) [view diff] no match in snippet view article find links to article

mathematician who lives in Germany, primarily known for his work in mathematical logic and set theory. Jensen completed a BA in economics at American University

List of theorems (6,293 words) [view diff] no match in snippet view article find links to article

theorem (mathematical logic) Conservativity theorem (mathematical logic) Craig's theorem (mathematical logic) Craig's interpolation theorem (mathematical logic)

Quantum logic (4,045 words) [view diff] no match in snippet view article find links to article

logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The formal system takes as its starting point an observation

Structuralism (philosophy of mathematics) (1,359 words) [view diff] no match in snippet view article

theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism

Wadge hierarchy (1,336 words) [view diff] no match in snippet view article find links to article

functions Borel–Wadge degrees. Analytical hierarchy – Concept in mathematical logic and set theory Arithmetical hierarchy – Hierarchy of complexity classes

Andrey Markov Jr. (353 words) [view diff] no match in snippet view article find links to article

mathematical logic and the foundations of mathematics. His name is in particular associated with Markov's principle and Markov's rule in mathematical

Logic (16,460 words) [view diff] no match in snippet view article find links to article

logic. Formal logic (also known as symbolic logic) is widely used in mathematical logic. It uses a formal approach to study reasoning: it replaces concrete

Formula (1,453 words) [view diff] no match in snippet view article find links to article

than 1, and the value true otherwise. (See Boolean expression) In mathematical logic, a formula (often referred to as a well-formed formula) is an entity

Index of logic articles (1,851 words) [view diff] no match in snippet view article find links to article

Apophasis -- Appeal to probability -- Appeal to ridicule -- Archive for Mathematical Logic -- Arché -- Argument -- Argument by example -- Argument form -- Argument

Rewriting (4,422 words) [view diff] no match in snippet view article find links to article

step comprises the previous example computation. In linguistics, phrase structure rules, also called rewrite rules, are used in some systems of generative

Heinrich Scholz (3,086 words) [view diff] no match in snippet view article find links to article

Scholz love of structure was also an important factor in his move into mathematical logic, describing it this: Scholz's feeling for structure was no small

Converse relation (1,725 words) [view diff] no match in snippet view article find links to article

relation to the converse relation is an involution, so it induces the structure of a semigroup with involution on the binary relations on a set, or, more

Association for Symbolic Logic (1,168 words) [view diff] no match in snippet view article find links to article

Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first

Jensen's covering theorem (349 words) [view diff] no match in snippet view article find links to article

first proof appeared in (Devlin & Jensen 1975). Silver later gave a fine-structure-free proof using his machines and finally Magidor (1990) gave an even

Type constructor (395 words) [view diff] no match in snippet view article find links to article

In the area of mathematical logic and computer science known as type theory, a type constructor is a feature of a typed formal language that builds new

Completeness of atomic initial sequents (116 words) [view diff] no match in snippet view article find links to article

and beta reduction. Typically it can be established by induction on the structure of A, much more easily than cut elimination. Gaisi Takeuti. Proof theory

Augustus De Morgan (6,988 words) [view diff] no match in snippet view article find links to article

as De Morgan's laws. Historically significant as the inception of mathematical logic, at the time, De Morgan's paper initiated a dispute with Hamilton

Herbrand interpretation (205 words) [view diff] no match in snippet view article find links to article

In mathematical logic, a Herbrand interpretation is an interpretation in which all constants and function symbols are assigned very simple meanings. Specifically

Turing degree (3,130 words) [view diff] no match in snippet view article find links to article

In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures

Theory of pure equality (761 words) [view diff] no match in snippet view article find links to article

In mathematical logic the theory of pure equality is a first-order theory. It has a signature consisting of only the equality relation symbol, and includes

Department of Mathematical Logic (Bulgarian Academy of Sciences) (473 words) [view diff] no match in snippet view article

The Department of Mathematical Logic at the Bulgarian Academy of Sciences was created by the Institute of Mathematics and Informatics in implementation

Residuated lattice (1,865 words) [view diff] no match in snippet view article find links to article

In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice x ≤ y and a monoid x•y which admits operations x\z

Omega-categorical theory (533 words) [view diff] no match in snippet view article find links to article

In mathematical logic, an omega-categorical theory is a theory that has exactly one countably infinite model up to isomorphism. Omega-categoricity is the

Ludics (489 words) [view diff] no match in snippet view article find links to article

ludics is an analysis of the principles governing inference rules of mathematical logic. Key features of ludics include notion of compound connectives, using

List of order theory topics (396 words) [view diff] no match in snippet view article find links to article

algebra (with involution) Łukasiewicz–Moisil algebra Boolean algebra (structure) Boolean ring Complete Boolean algebra Orthocomplemented lattice Quantale

Interpretability (171 words) [view diff] no match in snippet view article find links to article

In mathematical logic, interpretability is a relation between formal theories that expresses the possibility of interpreting or translating one into the

0† (328 words) [view diff] no match in snippet view article find links to article

of ordinals greater than κ, which together are indiscernible for the structure ( L , ∈ , U ) {\displaystyle (L,\in ,U)} , and 0† is defined to be the

Residuated Boolean algebra (1,155 words) [view diff] no match in snippet view article find links to article

mathematics, a residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the

Inner model (587 words) [view diff] no match in snippet view article find links to article

In set theory, a branch of mathematical logic, an inner model for a theory T is a substructure of a model M of a set theory that is both a model for T

Future of mathematics (1,959 words) [view diff] no match in snippet view article find links to article

2000, mathematical logic was discussed in "The Prospects For Mathematical Logic In The Twenty-First Century", including set theory, mathematical logic in

Nomos Alpha (367 words) [view diff] no match in snippet view article find links to article

style of music which makes use of set theory, abstract algebra, and mathematical logic in order to create and analyze musical compositions. Along with symbolic

Relation algebra (2,542 words) [view diff] no match in snippet view article find links to article

out in a manner familiar to all mathematicians, unlike the case in mathematical logic generally. RA can express any (and up to logical equivalence, exactly

Lévy hierarchy (1,393 words) [view diff] no match in snippet view article find links to article

In set theory and mathematical logic, the Lévy hierarchy, introduced by Azriel Lévy in 1965, is a hierarchy of formulas in the formal language of the Zermelo–Fraenkel

Indiscernibles (515 words) [view diff] no match in snippet view article find links to article

In mathematical logic, indiscernibles are objects that cannot be distinguished by any property or relation defined by a formula. Usually only first-order

Dedekind number (2,046 words) [view diff] no match in snippet view article find links to article

5–6, MR 0070608 Zaguia, Nejib (1993), "Isotone maps: enumeration and structure", in Sauer, N. W.; Woodrow, R. E.; Sands, B. (eds.), Finite and Infinite

Sy Friedman (343 words) [view diff] no match in snippet view article find links to article

of the Kurt Gödel Research Center for Mathematical Logic. His main research interest lies in mathematical logic, in particular in set theory and recursion

Categorical logic (1,104 words) [view diff] no match in snippet view article find links to article

tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science

Gödel Lecture (596 words) [view diff] no match in snippet view article find links to article

The Gödel Lecture is an honor in mathematical logic given by the Association for Symbolic Logic, associated with an annual lecture at the association's

Weak interpretability (238 words) [view diff] no match in snippet view article find links to article

In mathematical logic, weak interpretability is a notion of translation of logical theories, introduced together with interpretability by Alfred Tarski

Skolem arithmetic (1,957 words) [view diff] no match in snippet view article find links to article

In mathematical logic, Skolem arithmetic is the first-order theory of the natural numbers with multiplication, named in honor of Thoralf Skolem. The signature

Enumeration reducibility (1,437 words) [view diff] no match in snippet view article find links to article

mathematische Logik und Grundlagen der Mathematik (the predecessor of Mathematical Logic Quarterly) in 1959. Source: Let ( D u ) {\displaystyle (D_{u})} be

Kleene star (884 words) [view diff] no match in snippet view article find links to article

In mathematical logic and theoretical computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation on a set V to generate

Interior algebra (3,849 words) [view diff] no match in snippet view article find links to article

abstract algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras

Algorithm (7,016 words) [view diff] no match in snippet view article find links to article

van Heijenoort, Jean (2001). From Frege to Gödel, A Source Book in Mathematical Logic, 1879–1931 ((1967) ed.). Harvard University Press, Cambridge. ISBN 978-0-674-32449-7

Martin Grohe (547 words) [view diff] no match in snippet view article find links to article

computer scientist known for his research on parameterized complexity, mathematical logic, finite model theory, the logic of graphs, database theory, descriptive

Deep inference (251 words) [view diff] no match in snippet view article find links to article

In mathematical logic, deep inference names a general idea in structural proof theory that breaks with the classical sequent calculus by generalising the

BlooP and FlooP (696 words) [view diff] no match in snippet view article find links to article

cannot be written in BlooP. Borrowing from standard terminology in mathematical logic, Hofstadter calls FlooP's unbounded loops MU-loops. Like all Turing-complete

Programming paradigm (2,699 words) [view diff] no match in snippet view article find links to article

answer to a question about a system of facts and rules, uses explicit mathematical logic for programming reactive – a desired result is declared with data

Original proof of Gödel's completeness theorem (4,798 words) [view diff] no match in snippet view article find links to article

ideas faithfully, while restating the proof in the modern language of mathematical logic. This outline should not be considered a rigorous proof of the theorem

Per Martin-Löf (2,874 words) [view diff] no match in snippet view article find links to article

renowned for his work on the foundations of probability, statistics, mathematical logic, and computer science. Since the late 1970s, Martin-Löf's publications

Coherent space (1,222 words) [view diff] no match in snippet view article find links to article

coherence space A {\displaystyle {\mathcal {A}}} . This allows for some structure to be discussed on types. For instance, each term a {\displaystyle a}

Hrushovski construction (667 words) [view diff] no match in snippet view article find links to article

In model theory, a branch of mathematical logic, the Hrushovski construction generalizes the Fraïssé limit by working with a notion of strong substructure

Jacques Herbrand (722 words) [view diff] no match in snippet view article find links to article

by his professors Helmut Hasse and Richard Courant. He worked in mathematical logic and class field theory. He introduced recursive functions. Herbrand's

Structural proof theory (1,182 words) [view diff] no match in snippet view article find links to article

In mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof

Principle of compositionality (1,414 words) [view diff] no match in snippet view article find links to article

In semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is

Distributive property (2,998 words) [view diff] no match in snippet view article find links to article

rings, and fields. It is also encountered in Boolean algebra and mathematical logic, where each of the logical and (denoted ∧ {\displaystyle \,\land \

Distributive property (2,998 words) [view diff] no match in snippet view article find links to article

rings, and fields. It is also encountered in Boolean algebra and mathematical logic, where each of the logical and (denoted ∧ {\displaystyle \,\land \

Mivar-based approach (3,024 words) [view diff] no match in snippet view article find links to article

can take into consideration all the factors. Mivar computations use mathematical logic. In a simplified form they can be represented as implication in the

Calculus of structures (114 words) [view diff] no match in snippet view article find links to article

In mathematical logic, the calculus of structures is a proof calculus with deep inference for studying the structural proof theory of noncommutative logic

Bunched logic (2,856 words) [view diff] no match in snippet view article find links to article

in which the contexts Γ in an entailment judgement Γ ⊢ A are tree-like structures (bunches) rather than lists or (multi)sets as in most proof calculi. Bunched

Involution (mathematics) (2,240 words) [view diff] no match in snippet view article

transpositions. The involutions of a group have a large impact on the group's structure. The study of involutions was instrumental in the classification of finite

NIP (model theory) (580 words) [view diff] no match in snippet view article

In model theory, a branch of mathematical logic, a complete theory T is said to satisfy NIP ("not the independence property") if none of its formulae satisfy

String (computer science) (5,027 words) [view diff] no match in snippet view article

literal or an anonymous string. In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of

Morley rank (627 words) [view diff] no match in snippet view article find links to article

In mathematical logic, Morley rank, introduced by Michael D. Morley (1965), is a means of measuring the size of a subset of a model of a theory, generalizing

Normal form (natural deduction) (636 words) [view diff] no match in snippet view article

In mathematical logic and proof theory, a derivation in normal form in the context of natural deduction refers to a proof which contains no detours — steps

Automata theory (3,851 words) [view diff] no match in snippet view article find links to article

computer science with close connections to cognitive science and mathematical logic. The word automata comes from the Greek word αὐτόματος, which means

Kripke semantics (4,818 words) [view diff] no match in snippet view article find links to article

Constructive Propositional Logic — Kripke Semantics". Introduction to Mathematical Logic. University of Latvia. N.B: Constructive = intuitionistic. Garson

Algorithmic technique (913 words) [view diff] no match in snippet view article find links to article

algorithmic technique that uses two indices (or pointers) to traverse a data structure, usually an array or string, often from different ends or at different

Hub labels (276 words) [view diff] no match in snippet view article find links to article

that can be reached with an ascending search on the relative multi-level structure. The advantage of these distances is that they all represent the shortest

Abstract state machine (1,163 words) [view diff] no match in snippet view article find links to article

machine operating on states that are arbitrary data structures (structure in the sense of mathematical logic, that is a nonempty set together with a number

Albert Muchnik (346 words) [view diff] no match in snippet view article find links to article

Russian mathematician who worked in the field of foundations and mathematical logic. He received his Ph.D. from Moscow State Pedagogical Institute in

End extension (467 words) [view diff] no match in snippet view article find links to article

n {\displaystyle \Sigma _{n}} on the Lévy hierarchy, every countable structure in which Σ n {\displaystyle \Sigma _{n}} -collection holds has a Σ n {\displaystyle

Lindström quantifier (1,192 words) [view diff] no match in snippet view article find links to article

In mathematical logic, a Lindström quantifier is a generalized polyadic quantifier. Lindström quantifiers generalize first-order quantifiers, such as the

Laws of Form (6,798 words) [view diff] no match in snippet view article find links to article

unpublished until 2021, and further refined during subsequent lectures on mathematical logic he gave under the auspices of the University of London's extension

Löwenheim number (654 words) [view diff] no match in snippet view article find links to article

In mathematical logic the Löwenheim number of an abstract logic is the smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holds

Geometric group theory (4,308 words) [view diff] no match in snippet view article find links to article

geometry. There are also substantial connections with complexity theory, mathematical logic, the study of Lie groups and their discrete subgroups, dynamical systems

Container (type theory) (406 words) [view diff] no match in snippet view article

In type theory, a discipline within mathematical logic, containers are abstractions which permit various "collection types", such as lists and trees, to

Herbrand's theorem (787 words) [view diff] no match in snippet view article find links to article

Herbrand's theorem is a fundamental result of mathematical logic obtained by Jacques Herbrand (1930). It essentially allows a certain kind of reduction

Binary data (1,643 words) [view diff] no match in snippet view article find links to article

including bit (binary digit) in computer science, truth value in mathematical logic and related domains and binary variable in statistics. A discrete

Václav E. Beneš (1,186 words) [view diff] no match in snippet view article find links to article

doctorate in mathematics at Princeton University (1953) on a treatise on Mathematical logic. He then worked for Bell Labs until 1986, contributing to Kalman filter

Glossary of mathematical symbols (9,929 words) [view diff] no match in snippet view article find links to article

mathematics, and are listed here. For symbols that are used only in mathematical logic, or are rarely used, see List of logic symbols. ¬ (not sign) Denotes

Vladimir Kanovei (388 words) [view diff] no match in snippet view article find links to article

Information Transmission Problems in Moscow, Russia. His interests include mathematical logic and foundations, as well as mathematical history. Kanovei, Vladimir;

Computability in Analysis and Physics (616 words) [view diff] no match in snippet view article find links to article

Richards. It was published by Springer-Verlag in their Perspectives in Mathematical Logic series in 1989, and reprinted by the Association for Symbolic Logic

Sequent calculus (6,091 words) [view diff] no match in snippet view article find links to article

In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a

Polish notation (2,433 words) [view diff] no match in snippet view article find links to article

already. Alonzo Church mentions this notation in his classic book on mathematical logic as worthy of remark in notational systems even contrasted to Alfred

Ω-consistent theory (1,988 words) [view diff] no match in snippet view article find links to article

In mathematical logic, an ω-consistent (or omega-consistent, also called numerically segregative) theory is a theory (collection of sentences) that is

Mathematicism (2,393 words) [view diff] no match in snippet view article find links to article

Following Descartes, Leibniz attempted to derive connections between mathematical logic, algebra, infinitesimal calculus, combinatorics, and universal characteristics

Definite description (1,933 words) [view diff] no match in snippet view article find links to article

suppose, but rather an "incomplete symbol" that introduces quantificational structure into sentences in which it occurs. The sentence "the present King of France

Boolean domain (940 words) [view diff] no match in snippet view article find links to article

University Press. p. 99. Mendelson, Elliott (1997). Introduction to Mathematical Logic (4 ed.). Chapman & Hall/CRC. p. 11. Hehner, Eric C. R. (2010) [1993]

Grigori Mints (707 words) [view diff] no match in snippet view article find links to article

2014) was a Russian philosopher and mathematician who worked in mathematical logic. He was born in Leningrad, in the Soviet Union (now St. Petersburg

Admissible ordinal (660 words) [view diff] no match in snippet view article find links to article

Constructible Universe, p.95. Perspectives in Mathematical Logic, Springer-Verlag. J. Barwise, Admissible Sets and Structures (1976). Cambridge University Press

Beta-model (777 words) [view diff] no match in snippet view article find links to article

Rathjen, Proof theoretic analysis of KPM (1991), p.381. Archive for Mathematical Logic, Springer-Verlag. Accessed 28 February 2023. M. Rathjen, Admissible

Brouwer–Heyting–Kolmogorov interpretation (1,365 words) [view diff] no match in snippet view article find links to article

In mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, is an explanation of the meaning of proof in intuitionistic

Marcia Groszek (492 words) [view diff] no match in snippet view article find links to article

Jean Groszek is an American mathematician whose research concerns mathematical logic, set theory, forcing, and recursion theory. She is a professor of

Tennenbaum's theorem (1,081 words) [view diff] no match in snippet view article find links to article

Stanley Tennenbaum who presented the theorem in 1959, is a result in mathematical logic that states that no countable nonstandard model of first-order Peano

John Truss (1,358 words) [view diff] no match in snippet view article find links to article

University of Leeds where he specialises in mathematical logic, infinite permutation groups, homogeneous structures and model theory. Truss began his career

Filter (mathematics) (2,829 words) [view diff] no match in snippet view article

that cannot be enlarged, and describe nonconstructive techniques in mathematical logic. Filters on sets were introduced by Henri Cartan in 1937. Nicolas

Jean-Dominique Warnier (183 words) [view diff] no match in snippet view article find links to article

combines two disciplines: one scientific, by a rigorous application of mathematical logic; the other humanist, by the organization of a harmonious collaboration

Mathematics (15,938 words) [view diff] no match in snippet view article find links to article

century or had not previously been considered as mathematics, such as mathematical logic and foundations. Number theory began with the manipulation of numbers

Mai Gehrke (253 words) [view diff] no match in snippet view article find links to article

mathematician who studies the theory of lattices and their applications to mathematical logic and theoretical computer science. She is a director of research for

Exclusive or (3,354 words) [view diff] no match in snippet view article find links to article

Bussum, Pays-Bas. Translated as Bocheński, J. M. (1959). A Precis of Mathematical Logic. Translated by Bird, O. Dordrecht, Holland: D. Reidel Publishing Company

Truth (12,454 words) [view diff] no match in snippet view article find links to article

of topoi and other concepts from category theory in the study of mathematical logic. They provide a choice of formal semantics for intuitionistic logic

Polarity (227 words) [view diff] no match in snippet view article find links to article

a concept in geometry of the triangle Polarity of a literal, in mathematical logic Polarity (international relations), a description of the distribution

John Corcoran (logician) (2,379 words) [view diff] no match in snippet view article

the conceptual structure of logic, the metaphysical and epistemological presuppositions of logic, the nature of mathematical logic and the gaps between

Japaridze's polymodal logic (1,202 words) [view diff] no match in snippet view article find links to article

Icar, "On topological models of GLP". Ways of proof theory, Ontos Mathematical Logic, 2, eds. R. Schindler, Ontos Verlag, Frankfurt, 2010, pp. 133–153

Infinitesimal (5,092 words) [view diff] no match in snippet view article find links to article

becomes more difficult to say anything concrete about the hierarchical structure of infinities and infinitesimals. An example from category 1 above is

Saharon Shelah (1,646 words) [view diff] no match in snippet view article find links to article

at Rutgers University since 1986. Shelah's main interests lie in mathematical logic, model theory in particular, and in axiomatic set theory. In model

Binary decision (785 words) [view diff] no match in snippet view article find links to article

decisions are basic to many fields. Examples include: Truth values in mathematical logic, and the corresponding Boolean data type in computer science, representing

Geometric logic (596 words) [view diff] no match in snippet view article find links to article

In mathematical logic, geometric logic is an infinitary generalisation of coherent logic, a restriction of first-order logic due to Skolem that is proof-theoretically

Giorgi Japaridze (2,628 words) [view diff] no match in snippet view article find links to article

Archive for Mathematical Logic 53 (2014), pages 949-967. G. Japaridze, "The polymodal logic of provability". Intensional Logics and Logical Structure of Theories

Infinite-tree automaton (1,122 words) [view diff] no match in snippet view article find links to article

computer science and mathematical logic, an infinite-tree automaton is a state machine that deals with infinite tree structures. It can be seen as an

Modal logic (8,650 words) [view diff] no match in snippet view article find links to article

subsume relational ones, allowing non-normal modal logics. The extra structure they provide also allows a transparent way of modeling certain concepts

Combinatory logic (5,301 words) [view diff] no match in snippet view article find links to article

logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has

Graduate Texts in Mathematics (5,056 words) [view diff] no match in snippet view article find links to article

Humphreys (1975, ISBN 978-0-387-90108-4) An Algebraic Introduction to Mathematical Logic, Donald W. Barnes, John M. Mack (1975, ISBN 978-0-387-90109-1) Linear

Sort (148 words) [view diff] no match in snippet view article find links to article

Standard Template Library SORT (journal) Sort (mathematical logic), a domain in a many-sorted structure Sort (typesetting), a piece of metal type Sort

Mathematical psychology (3,095 words) [view diff] no match in snippet view article find links to article

vision and hearing). During the war, developments in engineering, mathematical logic and computability theory, computer science and mathematics, and the

Structural rule (592 words) [view diff] no match in snippet view article find links to article

Rule of mathematical logic

Jack Silver (489 words) [view diff] no match in snippet view article find links to article

(1971). "Some applications of model theory in set theory". Annals of Mathematical Logic 3(1), pp. 45–110. Silver, Jack H. (1973). "The bearing of large cardinals

Mereology (7,356 words) [view diff] no match in snippet view article find links to article

foundations". North-Holland: 1015–31. Goodman, Nelson, 1977 (1951). The Structure of Appearance. Kluwer. Goodman, Nelson, and Quine, Willard, 1947, "Steps

Declarative programming (2,373 words) [view diff] no match in snippet view article find links to article

referentially transparent). A language with a clear correspondence to mathematical logic. These definitions overlap substantially. Declarative programming

Hypersequent (1,971 words) [view diff] no match in snippet view article find links to article

In mathematical logic, the hypersequent framework is an extension of the proof-theoretical framework of sequent calculi used in structural proof theory

Alfred Foster (mathematician) (494 words) [view diff] no match in snippet view article

1971. Foster's Ph.D. dissertation and his first few papers were in mathematical logic. From this point, he soon focused on the related theory of Boolean

Pure inductive logic (4,462 words) [view diff] no match in snippet view article find links to article

Pure inductive logic (PIL) is the area of mathematical logic concerned with the philosophical and mathematical foundations of probabilistic inductive reasoning

Predicate functor logic (3,078 words) [view diff] no match in snippet view article find links to article

In mathematical logic, predicate functor logic (PFL) is one of several ways to express first-order logic (also known as predicate logic) by purely algebraic

Boolean algebras canonically defined (8,242 words) [view diff] no match in snippet view article find links to article

algebra thus permits applying the methods of abstract algebra to mathematical logic and digital logic. Unlike groups of finite order, which exhibit complexity

Abstract elementary class (1,724 words) [view diff] no match in snippet view article find links to article

In model theory, a discipline within mathematical logic, an abstract elementary class, or AEC for short, is a class of models with a partial order similar

Logical form (1,369 words) [view diff] no match in snippet view article find links to article

form with respect to whole arguments, as the schemata or inferential structure of the argument. In argumentation theory or informal logic, an argument

Second-order arithmetic (3,837 words) [view diff] no match in snippet view article find links to article

In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative

Forest informatics (894 words) [view diff] no match in snippet view article find links to article

Informatics Ecoinformatics Evolutionary informatics Geoinformatics Mathematical logic Graph theory Computational geometry Geographic Information Systems

Square principle (366 words) [view diff] no match in snippet view article find links to article

443. Jensen, R. Björn (1972), "The fine structure of the constructible hierarchy", Annals of Mathematical Logic, 4 (3): 229–308, doi:10.1016/0003-4843(72)90001-0

Topological Boolean algebra (148 words) [view diff] no match in snippet view article find links to article

Topological Boolean algebra may refer to: In abstract algebra and mathematical logic, topological Boolean algebra is one of the many names that have been

Boolean algebra (structure) (3,372 words) [view diff] no match in snippet view article

1960s, Paul Cohen, Dana Scott, and others found deep new results in mathematical logic and axiomatic set theory using offshoots of Boolean algebra, namely

Order theory (4,510 words) [view diff] no match in snippet view article find links to article

structures play a role in mathematical logic and especially Boolean algebras have major applications in computer science. Finally, various structures

David McGoveran (2,306 words) [view diff] no match in snippet view article find links to article

applications of mathematical logic has pervaded Mr. McGoveran's career (1971–present). He has done original research and published on the structure of paradoxes

Homotopy type theory (4,643 words) [view diff] no match in snippet view article find links to article

In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on

List of Boolean algebra topics (271 words) [view diff] no match in snippet view article find links to article

Boolean algebra and propositional logic. Algebra of sets Boolean algebra (structure) Boolean algebra Field of sets Logical connective Propositional calculus

Number sentence (286 words) [view diff] no match in snippet view article find links to article

(mathematics) Equation Inequality (mathematics) Open sentence Sentence (mathematical logic) Show Me That Number Sentence "Archived copy" (PDF). Archived from

George W. Brown (computer scientist) (1,138 words) [view diff] no match in snippet view article

his work and research in early computing machinery, game theory, mathematical logic, decision theory and administration. He was a major force in the design

Subtyping (4,046 words) [view diff] no match in snippet view article find links to article

holonymy. It is also related to the concept of bounded quantification in mathematical logic (see Order-sorted logic). Subtyping should not be confused with the

Surreal number (11,658 words) [view diff] no match in snippet view article find links to article

asked if it was possible to find a compatible ordered group or field structure. In 1962, Norman Alling used a modified form of Hahn series to construct

Erdős cardinal (767 words) [view diff] no match in snippet view article find links to article

Galvin, Fred (1978). "Generalized Erdős cardinals and 0#". Annals of Mathematical Logic. 15 (3): 289–313. doi:10.1016/0003-4843(78)90012-8. ISSN 0003-4843

Sheaf (mathematics) (11,083 words) [view diff] no match in snippet view article

have provided applications to mathematical logic and to number theory. In many mathematical branches, several structures defined on a topological space

János Bolyai Mathematical Institute (138 words) [view diff] no match in snippet view article find links to article

(head: Tibor Krisztin) Geometry (head: Árpád Kurusa) Set Theory and Mathematical Logic (head: Péter Hajnal) Stochastics (head: Gyula Pap) Official website

Ignacio Matte Blanco (2,172 words) [view diff] no match in snippet view article find links to article

aspects of experience. In applying the complexity and paradoxes of mathematical logic to psychoanalysis, he pioneered a coherent way of understanding the

Post's lattice (1,916 words) [view diff] no match in snippet view article find links to article

constant functions. E. L. Post, The two-valued iterative systems of mathematical logic, Annals of Mathematics studies, no. 5, Princeton University Press

Outline of academic disciplines (4,327 words) [view diff] no match in snippet view article find links to article

ethics, Value theory Normative ethics Virtue ethics Logic (outline) Mathematical logic Philosophical logic Meta-philosophy Metaphysics (outline) Philosophy

Parse tree (1,359 words) [view diff] no match in snippet view article find links to article

Malden, MA: Wiley-Blackwell. Chiswell, Ian and Wilfrid Hodges 2007. Mathematical logic. Oxford: Oxford University Press. Aho, A. V., Sethi, R., and Ullman

Category theory (3,896 words) [view diff] no match in snippet view article find links to article

For this reason, it is used throughout mathematics. Applications to mathematical logic and semantics (categorical abstract machine) came later. Certain categories

S2S (mathematics) (4,618 words) [view diff] no match in snippet view article

American Mathematical Society. 141. Janin, David; Lenzi, Giacomo. On the Structure of the Monadic Logic of the Binary Tree. MFCS 1999. doi:10.1007/3-540-48340-3_28

Loosely associated statements (250 words) [view diff] no match in snippet view article find links to article

infer a claim or conclusion, but because they lack a coherent logical structure any such interpretation is subjective as loosely associated statements

Assembly (realizability) (1,552 words) [view diff] no match in snippet view article

In theoretical computer science and mathematical logic, assemblies can be informally described as sets equipped with representations for elements. Realizability

Positivism dispute (1,519 words) [view diff] no match in snippet view article find links to article

explication of a purely formal conception of objectivity, and the use of mathematical logic to do so are not epistemological projects." In fact, they had already

Lists of mathematics topics (2,589 words) [view diff] no match in snippet view article find links to article

List of graph theory topics Logic is the foundation that underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning

Mathematics Subject Classification (1,395 words) [view diff] no match in snippet view article find links to article

mathematics and mathematical modeling.) 01: History and biography 03: Mathematical logic and foundations (including model theory, computability theory, set

Partial combinatory algebra (1,581 words) [view diff] no match in snippet view article find links to article

computer science and mathematical logic, specifically in realizability, a partial combinatory algebra (pca) is an algebraic structure which abstracts a model

Harry R. Lewis (4,524 words) [view diff] no match in snippet view article find links to article

theory of formal languages; its inclusion of complexity theory and mathematical logic was innovative for its time. It has been called an "excellent traditional

Liar paradox (4,462 words) [view diff] no match in snippet view article find links to article

Gödel's incompleteness theorems are two fundamental theorems of mathematical logic which state inherent limitations of sufficiently powerful axiomatic

Lie theory (1,253 words) [view diff] no match in snippet view article find links to article

subgroups generate the Lie algebra. The structure of a Lie group is implicit in its algebra, and the structure of the Lie algebra is expressed by root

Resolution (logic) (4,063 words) [view diff] no match in snippet view article

In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation-complete theorem-proving technique for sentences

Monoidal t-norm logic (3,718 words) [view diff] no match in snippet view article find links to article

In mathematical logic, monoidal t-norm based logic (or shortly MTL), the logic of left-continuous t-norms, is one of the t-norm fuzzy logics. It belongs

Autonomy of syntax (643 words) [view diff] no match in snippet view article find links to article

approaches, aimed at finding instances of semantically determined syntactic structures, to disprove the formalist argument of the autonomy of syntax. The principle

Willard Van Orman Quine (6,471 words) [view diff] no match in snippet view article find links to article

modal logic, and the non-logical character of higher-order logic. Mathematical Logic is based on Quine's graduate teaching during the 1930s and 1940s.

Gottlob Frege (5,402 words) [view diff] no match in snippet view article find links to article

Mathematica (3 vols.) appeared in 1910–13, the dominant approach to mathematical logic was still that of George Boole (1815–64) and his intellectual descendants

Walter Pitts (1,932 words) [view diff] no match in snippet view article find links to article

mathematical biophysics, remodeling biology on the structure of the physical sciences and mathematical logic. Pitts also worked closely with the mathematician

RecycleUnits (1,627 words) [view diff] no match in snippet view article find links to article

In mathematical logic, proof compression by RecycleUnits is a method for compressing propositional logic resolution proofs. Its main idea is to make use

In mathematical logic and theoretical computer science, a register machine is a generic class of abstract machines, analogous to a Turing machine and thus

Tarka-Sangraha (766 words) [view diff] no match in snippet view article find links to article

several generations. In Indian philosophical writings, the traditional structure of presenting a system consisted of three things: uddesa (listing of items

Alpha (1,477 words) [view diff] no match in snippet view article find links to article

in algebraic solutions representing quantities such as angles. In mathematical logic, α is sometimes used as a placeholder for ordinal numbers. It is used

Axiom of reducibility (6,052 words) [view diff] no match in snippet view article find links to article

affects the very foundations of reasoning..." By the time of his 1908 Mathematical logic as based on the theory of types Russell had studied "the contradictions"

SKI combinator calculus (3,236 words) [view diff] no match in snippet view article find links to article

ed. (2002) [1967]. "On the building blocks of mathematical logic". A Source Book in Mathematical Logic 1879–1931. Harvard University Press. pp. 355–366

Logic of graphs (5,029 words) [view diff] no match in snippet view article find links to article

with formal specifications of graph properties using sentences of mathematical logic. There are several variations in the types of logical operation that

Alfred North Whitehead (14,536 words) [view diff] no match in snippet view article find links to article

considered one of the twentieth century's most important works in mathematical logic, and placed 23rd in a list of the top 100 English-language nonfiction

Elementary recursive function (1,025 words) [view diff] no match in snippet view article find links to article

(2002). "Plain Bases for Classes of Primitive Recursive Functions". Mathematical Logic Quarterly. 48: 93–104. doi:10.1002/1521-3870(200201)48:1<93::aid-malq93>3

Borel equivalence relation (317 words) [view diff] no match in snippet view article find links to article

Annals of Mathematical Logic. 18 (1): 1–28. doi:10.1016/0003-4843(80)90002-9. Kanovei, Vladimir; Borel equivalence relations. Structure and classification

Robert Lawson Vaught (427 words) [view diff] no match in snippet view article find links to article

the supervision of Alfred Tarski, completing in 1954 a thesis on mathematical logic, titled Topics in the Theory of Arithmetical Classes and Boolean Algebras

Discrete mathematics (2,771 words) [view diff] no match in snippet view article find links to article

on graph theory and mathematical logic. Included within theoretical computer science is the study of algorithms and data structures. Computability studies

Diamond principle (692 words) [view diff] no match in snippet view article find links to article

PMID 15131270. Jensen, R. Björn (1972). "The fine structure of the constructible hierarchy". Annals of Mathematical Logic. 4 (3): 229–308. doi:10.1016/0003-4843(72)90001-0

Knowledge representation and reasoning (5,354 words) [view diff] no match in snippet view article find links to article

automated theorem-provers for first-order logic, motivated by the use of mathematical logic to formalise mathematics and to automate the proof of mathematical

Ernest Nagel (1,076 words) [view diff] no match in snippet view article find links to article

explicating Gödel's incompleteness theorems to those not well trained in mathematical logic. He edited the Journal of Philosophy (1939–1956) and the Journal of

Index of philosophical literature (6,113 words) [view diff] no match in snippet view article find links to article

Archiv für Rechts- und Sozialphilosophie – Archive Fever – Archive for Mathematical Logic – Areopagitica – Aristotle for Everybody – Ars Disputandi – Art as

Pareto principle (2,723 words) [view diff] no match in snippet view article find links to article

causes is based upon a combination of an empirical principle and mathematical logic. The empirical principle is usually known as the Pareto principle

Leon Henkin (10,251 words) [view diff] no match in snippet view article find links to article

courses he taught were directly related to his research area, such as "Mathematical Logic", "Metamathematics" or "Cylindric Algebra", but others extended to

Robert Le Ricolais (1,567 words) [view diff] no match in snippet view article find links to article

engineer considered one of the creators of the spatial structure principle, based on mathematical logic and observation of nature. He studied and worked in

Programming language theory (1,613 words) [view diff] no match in snippet view article find links to article

were developed thus allowing computer programs to be expressed as mathematical logic. A team of scientists at Xerox PARC led by Alan Kay develop Smalltalk

Self-reference (2,130 words) [view diff] no match in snippet view article find links to article

Drucker, Thomas (4 January 2008). Perspectives on the History of Mathematical Logic. Springer Science & Business Media. p. 110. ISBN 978-0-8176-4768-1

Criticism of nonstandard analysis (3,520 words) [view diff] no match in snippet view article find links to article

greatly. Paul Halmos described it as a technical special development in mathematical logic. Terence Tao summed up the advantage of the hyperreal framework by

Outline of discrete mathematics (1,824 words) [view diff] no match in snippet view article find links to article

mathematics a study of graphs – Vertices connected in pairs by edges Mathematical logic – Subfield of mathematics Discrete optimization – Branch of mathematical

Principle of explosion (1,264 words) [view diff] no match in snippet view article find links to article

Retrieved January 14, 2017. de Swart, Harrie (2018). Philosophical and Mathematical Logic. Springer. p. 47. Gamut, L. T. F. (1991). Logic, Language and Meaning

Natural number (5,889 words) [view diff] no match in snippet view article find links to article

(1993). "A theory of sets with the negation of the axiom of infinity". Mathematical Logic Quarterly. 39 (3): 338–352. doi:10.1002/malq.19930390138. MR 1270381

Universal algebra (3,006 words) [view diff] no match in snippet view article find links to article

lattices, and homomorphism theorems. Although the development of mathematical logic had made applications to algebra possible, they came about slowly;

Moti Gitik (332 words) [view diff] no match in snippet view article find links to article

extenders and negations of the Shelah Weak Hypothesis". Journal of Mathematical Logic. 20 (3): 2050013. doi:10.1142/S0219061320500130. S2CID 46948714. List

Pure mathematics (1,828 words) [view diff] no match in snippet view article find links to article

Generalizing theorems or mathematical structures can lead to deeper understanding of the original theorems or structures Generality can simplify the presentation

Arc pair grammar (1,121 words) [view diff] no match in snippet view article find links to article

Johnson and Paul Postal attempted to lay down a version of it using mathematical logic. This attempt swelled into a new theory, now known as APG. APG itself

Pure function (1,233 words) [view diff] no match in snippet view article find links to article

the result Lambda calculus – Mathematical-logic system based on functions Purely functional data structure – Data structure implementable in purely functional

Abstract algebra (4,336 words) [view diff] no match in snippet view article find links to article

is the study of algebraic structures, which are sets with specific operations acting on their elements. Algebraic structures include groups, rings, fields

Outline of computer science (1,036 words) [view diff] no match in snippet view article find links to article

discrete structures. Used in digital computer systems. Graph theory – Foundations for data structures and searching algorithms. Mathematical logic – Boolean

Abstract algebra (4,336 words) [view diff] no match in snippet view article find links to article

is the study of algebraic structures, which are sets with specific operations acting on their elements. Algebraic structures include groups, rings, fields

Resolution proof reduction via local context rewriting (1,086 words) [view diff] no match in snippet view article find links to article

In proof theory, an area of mathematical logic, resolution proof reduction via local context rewriting is a technique for resolution proof reduction via

Outline of algebraic structures (2,223 words) [view diff] no match in snippet view article find links to article

algebra The quaternions and more generally geometric algebras In Mathematical logic: Boolean algebras are both rings and lattices, under their two operations

Tuna Altınel (3,048 words) [view diff] no match in snippet view article find links to article

Lyon 1 in France since 1996. He is a specialist in group theory and mathematical logic. With Alexandre Borovik and Gregory Cherlin, he proved a major case

Richard Boyd (1,493 words) [view diff] no match in snippet view article find links to article

Cartwright, went on to earn his Ph.D in 1970 with a doctoral thesis on mathematical logic titled A Recursion-Theoretic Characterization of the Ramified Analytical

Ring of modular forms (1,060 words) [view diff] no match in snippet view article find links to article

forms of Γ. The study of rings of modular forms describes the algebraic structure of the space of modular forms. Let Γ be a subgroup of SL(2, Z) that is

Hyperfinite equivalence relation (1,671 words) [view diff] no match in snippet view article find links to article

"Cardinal characteristics and countable Borel equivalence relations", Mathematical Logic Quarterly, 63 (3–4): 211–227, arXiv:1103.2312, doi:10.1002/malq.201400111

Many-valued logic (3,346 words) [view diff] no match in snippet view article find links to article

Multiple-Valued Logic and Soft Computing. Philosophy portal Psychology portal Mathematical logic Degrees of truth Fuzzy logic Gödel logic Jaina seven-valued logic

Derivative algebra (127 words) [view diff] no match in snippet view article find links to article

In mathematics: In abstract algebra and mathematical logic a derivative algebra is an algebraic structure that provides an abstraction of the derivative

Alexander Zinoviev (20,132 words) [view diff] no match in snippet view article find links to article

covering a number of areas of knowledge: sociology, social philosophy, mathematical logic, ethics, political thought. Most of his work is difficult to attribute

Scheme (programming language) (8,206 words) [view diff] no match in snippet view article

a complete calculation rule. It is helpful for the analysis using mathematical logic and tools. In this system, calculation can be seen as a directional

Reductionism (3,263 words) [view diff] no match in snippet view article find links to article

reduction is a foundational and central concept, not only in the realm of mathematical logic and abstract computation in computability (or recursive) theory, where

Guarded logic (812 words) [view diff] no match in snippet view article find links to article

guarded logic there were two major terms used to interpret modal logic. Mathematical logic and database theory (Artificial Intelligence) were first-order predicate

Named set theory (1,919 words) [view diff] no match in snippet view article find links to article

named sets", Modern Logic. International Journal for the History of Mathematical Logic, Set Theory, and Foundations of Mathematics 2 (1): 1–2, ISSN 1047-5982

Erlangen program (1,913 words) [view diff] no match in snippet view article find links to article

groupoids in geometry is considered in the article below by Pradines. In mathematical logic, the Erlangen program also served as an inspiration for Alfred Tarski

Colon (punctuation) (4,713 words) [view diff] no match in snippet view article

The combination with an equal sign (≔) is used for definitions. In mathematical logic, when using set-builder notation for describing the characterizing

David Gale (851 words) [view diff] no match in snippet view article find links to article

perfect information. This work led to fundamental contributions to mathematical logic. Gale is the inventor of the game of Bridg-It (also known as "Game

Dorothy Maud Wrinch (2,535 words) [view diff] no match in snippet view article find links to article

1916–1917, Wrinch took the Cambridge Moral Sciences tripos and studied mathematical logic with Russell in London. In December she was invited to Garsington

Wolf Prize in Mathematics (256 words) [view diff] no match in snippet view article find links to article

Saharon Shelah Israel for his many fundamental contributions to mathematical logic and set theory, and their applications within other parts of mathematics

Glossary of computer science (23,955 words) [view diff] no match in snippet view article find links to article

computer science). automated reasoning An area of computer science and mathematical logic dedicated to understanding different aspects of reasoning. The study

Space (mathematics) (9,328 words) [view diff] no match in snippet view article

non-isomorphic; their theory is multivalent. A similar idea occurs in mathematical logic: a theory is called categorical if all its models of the same cardinality

Leopold Kronecker (1,402 words) [view diff] no match in snippet view article find links to article

van Heijenoort, Jean (1977), From Frege to Gödel A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, ISBN 978-0-674-32449-7 Weber

Algebraically closed field (1,838 words) [view diff] no match in snippet view article find links to article

introduction to first-order logic". In Barwise, Jon (ed.). Handbook of Mathematical Logic. Studies in Logic and the Foundations of Mathematics. North Holland

Ieke Moerdijk (832 words) [view diff] no match in snippet view article find links to article

theory, algebraic and differential topology, and their applications to mathematical logic. Moerdijk is seen, together with André Joyal, as one of the founders

Actor model later history (1,443 words) [view diff] no match in snippet view article find links to article

Some of these authors made claims that these systems were based on mathematical logic. However, like the Actor model, the Prolog-like concurrent systems

Fixed point (mathematics) (1,696 words) [view diff] no match in snippet view article

\operatorname {\mathsf {fix}} f=f(\operatorname {\mathsf {fix}} f).} In mathematical logic, fixed-point logics are extensions of classical predicate logic that

Borel determinacy theorem (2,061 words) [view diff] no match in snippet view article find links to article

Friedman, "Higher set theory and mathematical practice", Annals of Mathematical Logic 2 (1971). pp.326--357. Leinster, Tom (23 July 2021). "Borel Determinacy

Descriptive complexity theory (2,543 words) [view diff] no match in snippet view article find links to article

second-order logic. This connection between complexity and the logic of finite structures allows results to be transferred easily from one area to the other, facilitating

Andrey Kolmogorov (2,791 words) [view diff] no match in snippet view article find links to article

several departments: probability, statistics, and random processes; mathematical logic. He also served as the Dean of the Moscow State University Department

Algebraic geometry and analytic geometry (2,782 words) [view diff] no match in snippet view article find links to article

principle and its proof are due to Alfred Tarski and are based in mathematical logic. This principle permits the carrying over of some results obtained

Empiricism (6,689 words) [view diff] no match in snippet view article find links to article

experience as the basis for knowledge) with certain insights from mathematical logic that had been developed by Gottlob Frege and Ludwig Wittgenstein.

Wolfgang Stegmüller (966 words) [view diff] no match in snippet view article find links to article

Carnap on semantics and logics as well as those of Kurt Gödel on mathematical logic. Later similar works are on Die Antinomien und ihre Behandlung (Antinomies

Arithmetic geometry (1,464 words) [view diff] no match in snippet view article find links to article

characterized by height functions which measure their arithmetic complexity. The structure of algebraic varieties defined over non-algebraically closed fields has

Sigma (2,191 words) [view diff] no match in snippet view article find links to article

3 + 4 + 5 = 15 {\displaystyle \sum _{k=0}^{5}k=0+1+2+3+4+5=15} In mathematical logic, Σ n 0 {\displaystyle \Sigma _{n}^{0}} is used to denote the set of

Systems theory in anthropology (4,727 words) [view diff] no match in snippet view article find links to article

interdisciplinary approach that included communication theory, cybernetics, and mathematical logic. In his collection of essays, The Sacred Unity, Bateson argues that

Analytic philosophy (10,877 words) [view diff] no match in snippet view article find links to article

of mathematics, philosophy of science, modern predicate logic and mathematical logic. The proliferation of analysis in philosophy began around the turn

Typing rule (811 words) [view diff] no match in snippet view article find links to article

that can be proven to specify the same typing relation. Judgment (mathematical logic) Type system Type theory Curry–Howard correspondence Sequent calculus

N.I. Lobachevsky Institute of Mathematics and Mechanics (402 words) [view diff] no match in snippet view article find links to article

Mathematics: Department of General Mathematics Department of Algebra and Mathematical Logic Department of Geometry Department of Mathematical Analysis Department

Zero sharp (1,679 words) [view diff] no match in snippet view article find links to article

(1971). "Some applications of model theory in set theory". Annals of Mathematical Logic. 3 (1): 45–110. doi:10.1016/0003-4843(71)90010-6. MR 0409188. Solovay

Saint Petersburg Academic University (762 words) [view diff] no match in snippet view article find links to article

courses in algorithms, computational complexity, discrete mathematics, mathematical logic, cryptography and numerous more specialized subjects of contemporary

Large countable ordinal (5,516 words) [view diff] no match in snippet view article find links to article

Jon (1976). Admissible Sets and Structures: an Approach to Definability Theory. Perspectives in Mathematical Logic. Springer-Verlag. ISBN 3-540-07451-1

Theoretical computer science (4,803 words) [view diff] no match in snippet view article find links to article

description: TCS covers a wide variety of topics including algorithms, data structures, computational complexity, parallel and distributed computation, probabilistic

Tree (set theory) (1,558 words) [view diff] no match in snippet view article

202–208, doi:10.1007/978-3-0348-9259-9_18. Monk, J. Donald (1976). Mathematical Logic. New York: Springer-Verlag. p. 517. ISBN 0-387-90170-1. Jech, Thomas

Combinatorics (3,524 words) [view diff] no match in snippet view article find links to article

combinatorics to infinite sets. It is a part of set theory, an area of mathematical logic, but uses tools and ideas from both set theory and extremal combinatorics

Combinatorics (3,524 words) [view diff] no match in snippet view article find links to article

combinatorics to infinite sets. It is a part of set theory, an area of mathematical logic, but uses tools and ideas from both set theory and extremal combinatorics

Simple non-inferential passage (556 words) [view diff] no match in snippet view article find links to article

imply a claim or conclusion, but because they lack a coherent logical structure any such interpretation is subjective as loosely associated statements

Name (2,636 words) [view diff] no match in snippet view article find links to article

government IDs, credit cards, etc.) are not random but have an internal structure and convention. Virtually all organizations that assign names or numbers

José Ferrater Mora (1,549 words) [view diff] no match in snippet view article find links to article

Questions: Essays on Philosophy (Madrid: Revista de Occidente, 1955) Mathematical Logic (Mexico: Fondo de Cultura Económica, 1955), co-authored with Hugues

History of mathematical notation (11,251 words) [view diff] no match in snippet view article find links to article

equation, and can build a concept structure which has no relation to reality. Some of the introduced mathematical logic notation during this time included

Romanian philosophy (11,463 words) [view diff] no match in snippet view article find links to article

"logistic", i.e., in the terminology of the epoch, mathematical logic. He actually rejected mathematical logic, thinking it is reductive even in comparison

Programming language (7,415 words) [view diff] no match in snippet view article find links to article

combination of regular expressions (for lexical structure) and Backus–Naur form (for grammatical structure). Below is a simple grammar, based on Lisp: expression

Mathematical model (4,766 words) [view diff] no match in snippet view article find links to article

itself a branch of mathematics and does not necessarily conform to any mathematical logic, but is typically a branch of some science or other technical subject

Numerical algebraic geometry (1,306 words) [view diff] no match in snippet view article find links to article

Multi-homogeneous and beyond these, specific start systems that closely mirror the structure of f {\displaystyle f} may be formed for particular systems. The choice

Dyadic rational (3,895 words) [view diff] no match in snippet view article find links to article

Robert (2004), "Weak computability and representation of reals", Mathematical Logic Quarterly, 50 (4–5): 431–442, doi:10.1002/malq.200310110, MR 2090389

Elliott Jaques (1,837 words) [view diff] no match in snippet view article find links to article

in Logic and Human Action: A theory of discontinuity in the structure of mathematical logic, psychological behaviour, and social organisation. (London:

Categorial grammar (3,689 words) [view diff] no match in snippet view article find links to article

Ajdukiewicz (in 1935) and other scholars from the Polish tradition of mathematical logic including Stanisław Leśniewski, Emil Post and Alfred Tarski. Ajdukiewicz's

Expressive power (computer science) (1,000 words) [view diff] no match in snippet view article

description of languages and their meaning, such as formal language theory, mathematical logic and process algebra. In informal discussions, the term often refers

Patrick Suppes (1,422 words) [view diff] no match in snippet view article find links to article

Structures. CSLI (distributed by the University of Chicago Press). Suppes, Patrick; Hill, Shirley (2002) (1964). A First Course in Mathematical Logic

Department of Mathematics, University of Manchester (1,613 words) [view diff] no match in snippet view article find links to article

areas of algebra, analysis, noncommutative geometry, ergodic theory, mathematical logic, number theory, geometry and topology; and the more applied dynamical

History of the function concept (10,688 words) [view diff] no match in snippet view article find links to article

mathematical logic in van Heijenoort 1967, p. 359 commentary by W. V. Quine preceding Schönfinkel (1924) On the building blocks of mathematical logic

1910 in science (1,792 words) [view diff] no match in snippet view article find links to article

Bertrand Russell, one of the most important and seminal works in mathematical logic and philosophy. First known use of the term "Econometrics" (in cognate

Bayesian statistics (2,480 words) [view diff] no match in snippet view article find links to article

numerical and visual summaries. Bayesian epistemology For a list of mathematical logic notation used in this article Notation in probability and statistics

Begging the question (3,457 words) [view diff] no match in snippet view article find links to article

the cognitive abilities of humans. It is primarily a reflection of the structure of noncognitive reality. In short, a successful resolution of such a fallacy

University of Turin (4,378 words) [view diff] no match in snippet view article find links to article

Nobel Prize in Physiology or Medicine Giuseppe Peano, founder of mathematical logic and set theory Tullio Regge, physicist Maria Grazia Roncarolo, George

Planner (programming language) (2,311 words) [view diff] no match in snippet view article

would be unable to prove not P even though it follows by the rules of mathematical logic. This is an illustration of the fact that Prolog (like Planner) is

Formal semantics (natural language) (5,369 words) [view diff] no match in snippet view article

philosophy, while also incorporating work from computer science, mathematical logic, and cognitive psychology. Formal semanticists typically adopt an

Gödel operation (955 words) [view diff] no match in snippet view article find links to article

Sets and Structures. Perspectives in Mathematical Logic. Springer-Verlag. ISBN 3-540-07451-1. K. Devlin, An introduction to the fine structure of the constructible

List of fallacies (6,841 words) [view diff] no match in snippet view article find links to article

fallacies are challenging to classify. They can be classified by their structure (formal fallacies) or content (informal fallacies). Informal fallacies

Glossary of arithmetic and diophantine geometry (4,753 words) [view diff] no match in snippet view article find links to article

General rationality theorems are now known, drawing on methods of mathematical logic. Infinite descent Infinite descent was Pierre de Fermat's classical

Field (mathematics) (10,305 words) [view diff] no match in snippet view article

not isomorphic as topological fields). In model theory, a branch of mathematical logic, two fields E and F are called elementarily equivalent if every mathematical

Modus ponens (2,386 words) [view diff] no match in snippet view article find links to article

one is also true. If P implies Q and P is true, then Q is true. In mathematical logic, algebraic semantics treats every sentence as a name for an element

History of topos theory (1,642 words) [view diff] no match in snippet view article find links to article

(classifying toposes). They involve links between category theory and mathematical logic, and also (as a high-level, organisational discussion) between category

Plankalkül (2,743 words) [view diff] no match in snippet view article find links to article

by Hilbert's and Ackermann's book on elementary mathematical logic (see Principles of Mathematical Logic).: 113, 152, 216 To describe logical circuits

Józef Maria Bocheński (3,619 words) [view diff] no match in snippet view article find links to article

improving this logical structure with the most advanced logical tools available at the time, namely those of modern mathematical logic, then called ‘logistic’

Partial function (2,055 words) [view diff] no match in snippet view article find links to article

ISBN 978-0-8176-4186-3. Neal Koblitz; B. Zilber; Yu. I. Manin (2009). A Course in Mathematical Logic for Mathematicians. Springer Science & Business Media. p. 290.

Jordan curve theorem (3,351 words) [view diff] no match in snippet view article find links to article

Schönflies theorem in weak second-order arithmetic", Archive for Mathematical Logic, 46 (5): 465–480, doi:10.1007/s00153-007-0050-6, ISSN 0933-5846, MR 2321588

Solid modeling (3,497 words) [view diff] no match in snippet view article find links to article

2010. Ziegler, M. (2004). "Computable Operators on Regular Sets". Mathematical Logic Quarterly. 50 (45). Wiley: 392–404. doi:10.1002/malq.200310107. S2CID 17579181

Finite geometry (2,841 words) [view diff] no match in snippet view article find links to article

projective spaces. More abstractly, it can be defined as an incidence structure (P, L, I) consisting of a set P of points, a set L of lines, and an incidence

Donkey sentence (2,400 words) [view diff] no match in snippet view article find links to article

situation in which gender is typically unknown Lambda calculus – Mathematical-logic system based on functions Montague grammar – Approach to natural language

Database (9,858 words) [view diff] no match in snippet view article find links to article

optimization, depended on the fact that queries were expressed in terms of mathematical logic. Codd's paper inspired teams at various universities to research the

19th century in science (4,618 words) [view diff] no match in snippet view article find links to article

only numbers were 0 and 1. Boolean algebra is the starting point of mathematical logic and has important applications in computer science. Augustin-Louis

Necessity and sufficiency (2,394 words) [view diff] no match in snippet view article find links to article

necessary or sufficient, rather that categories resemble a family tree structure. To say that P is necessary and sufficient for Q is to say two things:

Werner Kaegi (composer) (1,456 words) [view diff] no match in snippet view article

From six years he received clarinet and piano lessons. He studied mathematical logic and music in Zürich, Heidelberg and Basel, and music composition in

Constructivism (philosophy of mathematics) (2,608 words) [view diff] no match in snippet view article

Sjerp (1977a). "Aspects of Constructive Mathematics". Handbook of Mathematical Logic. Studies in Logic and the Foundations of Mathematics. 90: 973–1052

Vladimir Karapetoff (968 words) [view diff] no match in snippet view article find links to article

mathematics. Certain postulates are made and a structure is built step by step on these, using mathematical logic and its recognized tools and operations. In

Greek letters used in mathematics, science, and engineering (6,018 words) [view diff] no match in snippet view article find links to article

independence number of a graph a placeholder for ordinal numbers in mathematical logic a type of receptor for the neurotransmitter noradrenaline in neuroscience

Nicolas Bourbaki (11,924 words) [view diff] no match in snippet view article find links to article

logicians, and therefore the collective had a limited interest in mathematical logic. As Bourbaki's members themselves said of the book on set theory,

Doctrine (mathematics) (413 words) [view diff] no match in snippet view article

"Doctrines in Categorical Logic". In Barwise, Jon (ed.). Handbook of Mathematical Logic. Elsevier Science Publishers B.V. pp. 283–313. doi:10.1016/S0049-237X(08)71104-2

Topos (4,308 words) [view diff] no match in snippet view article find links to article

category theory. They should be suitable for those knowing little mathematical logic and set theory, even non-mathematicians. Lawvere, F. William; Schanuel

Istituto Nazionale di Alta Matematica Francesco Severi (1,244 words) [view diff] no match in snippet view article find links to article

geometry and Topology; Algebraic Geometry and Commutative Algebra; and Mathematical Logic and applications. See the Italian law (La Camera dei Deputati & Il

Siegel modular variety (1,147 words) [view diff] no match in snippet view article find links to article

principally polarized abelian varieties of dimension g with a level n-structure, arises as the quotient of the Siegel upper half-space by the action of

Unifying theories in mathematics (1,846 words) [view diff] no match in snippet view article find links to article

is still taught that way. It was a parallel to the development of mathematical logic as a stand-alone branch of mathematics. By the 1930s symbolic logic

Pattern recognition (4,354 words) [view diff] no match in snippet view article find links to article

original on 2018-11-06. Retrieved 2018-11-06. Ian., Chiswell (2007). Mathematical logic, p. 34. Oxford University Press. ISBN 9780199215621. OCLC 799802313

John von Neumann (23,699 words) [view diff] no match in snippet view article find links to article

Van Heijenoort, Jean (1967). From Frege to Gödel: a Source Book in Mathematical Logic, 1879–1931. Cambridge, Massachusetts: Harvard University Press.

Cognitive linguistics (3,346 words) [view diff] no match in snippet view article find links to article

language as an autonomous mind module. Thus, language is separated from mathematical logic to the extent that inference cannot explain language acquisition.

Conceptual model (3,737 words) [view diff] no match in snippet view article find links to article

(classes of) mathematical structures such as groups, fields, graphs, or even universes of set theory, using tools from mathematical logic. A system that gives

History of the Actor model (2,771 words) [view diff] no match in snippet view article find links to article

physics in contrast with other models of computation that were based on mathematical logic, set theory, algebra, etc. Physics influenced the Actor model in many

Logo (programming language) (2,516 words) [view diff] no match in snippet view article

Seymour Papert. Its intellectual roots are in artificial intelligence, mathematical logic and developmental psychology. For the first four years of Logo research

Cardinal characteristic of the continuum (1,573 words) [view diff] no match in snippet view article find links to article

Baumgartner and Richard Laver. Iterated perfect-set forcing. Annals of Mathematical Logic 17 (1979) pp 271–288. Eric van Douwen. The Integers and Topology.

History of philosophy in Poland (6,870 words) [view diff] no match in snippet view article find links to article

the history of philosophy, the theory of knowledge, and especially mathematical logic. Jan Łukasiewicz gained world fame with his concept of many-valued

Rudolf Carnap (6,188 words) [view diff] no match in snippet view article find links to article

one of the very few students to attend Gottlob Frege's courses in mathematical logic. During his university years, he became enthralled with the German

Formalism (linguistics) (2,617 words) [view diff] no match in snippet view article

non-imaginary numbers, addition, subtraction, and so on. Based on mathematical logic, Husserl also created a "formal semantics" arguing that linguistic

Albert Wohlstetter (4,451 words) [view diff] no match in snippet view article find links to article

program after only one year. He stayed at Columbia to pursue a Ph.D. in mathematical logic and the philosophy of science where he studied under Abraham Wald

Image (mathematics) (2,437 words) [view diff] no match in snippet view article

An alternative notation for f [ A ] {\displaystyle f[A]} used in mathematical logic and set theory is f ″ A . {\displaystyle f\,''A.} Some texts refer

Collective intelligence (15,272 words) [view diff] no match in snippet view article find links to article

parallel, and distributed computational process, run in mathematical logic by the social structure. In this model, beings and information are modeled as

University of Antioquia (2,158 words) [view diff] no match in snippet view article find links to article

components, Reading Proficiency Test (Spanish) and Logical Reasoning Test (Mathematical Logic) and is equal to the candidates of all programs except for the Faculty

Existential graph (2,957 words) [view diff] no match in snippet view article find links to article

first edition of David Hilbert and Wilhelm Ackermann's Principles of Mathematical Logic. Add to the syntax of alpha a second kind of simple closed curve,

French philosophy (5,337 words) [view diff] no match in snippet view article find links to article

science concerned with the axiomatic method, formalism, set theory and mathematical logic. Jules Vuillemin (1920–2001) introduced the concept of the philosophy

Congruence lattice problem (5,500 words) [view diff] no match in snippet view article find links to article

first-order resolution in mathematical logic. Could this analogy be pushed further?) The proof of the theorem above runs by setting a structure theorem for congruence

L. E. J. Brouwer (2,156 words) [view diff] no match in snippet view article find links to article

Heijenoort, 1967 3rd printing 1976 with corrections, A Source Book in Mathematical Logic, 1879-1931. Harvard University Press, Cambridge MA, ISBN 0-674-32449-8

Zellig Harris (7,307 words) [view diff] no match in snippet view article find links to article

the notion of rules of transformation vs. rules of formation from mathematical logic. The terms originated with Rudolf Carnap. He was also introduced to

History of mathematics (16,327 words) [view diff] no match in snippet view article find links to article

only numbers were 0 and 1. Boolean algebra is the starting point of mathematical logic and has important applications in electrical engineering and computer

List of publications in mathematics (10,426 words) [view diff] no match in snippet view article find links to article

entirely in a formalized language. It contained a description of mathematical logic and many important theorems in other branches of mathematics. Many

Glossary of logic (30,237 words) [view diff] no match in snippet view article find links to article

legitimate mathematical structure, whether that structure is definable or not. combinatory logic A branch of mathematical logic that seeks to eliminate

Alpha recursion theory (1,455 words) [view diff] no match in snippet view article find links to article

October 12, 2021 R. Gostanian, The Next Admissible Ordinal, Annals of Mathematical Logic 17 (1979). Accessed 1 January 2023. Srebrny, Marian, Relatively constructible

Argumentation theory (7,363 words) [view diff] no match in snippet view article find links to article

to evade the challenge provided. Typically an argument has an internal structure, comprising the following: a set of assumptions or premises, a method

Dynamical systems theory (2,927 words) [view diff] no match in snippet view article find links to article

formed macroscopic and microscopic structures support each other, speeding up the process. These links form the structure of a new state of order in the mind

Abductive reasoning (9,972 words) [view diff] no match in snippet view article find links to article

logic as a normative field in philosophy, not in purely formal or mathematical logic, and eventually as a topic also in economics of research. As two stages

Alan T. Waterman Award (2,948 words) [view diff] no match in snippet view article find links to article

phenomena, and his fundamental contributions to virtually all areas of mathematical logic. 1983 Corey S. Goodman (de) For his contributions to our understanding

Trakhtenbrot's theorem (1,929 words) [view diff] no match in snippet view article find links to article

the finite. This proof is taken from Chapter 10, section 4, 5 of Mathematical Logic by H.D. Ebbinghaus. As in the most common proof of Gödel's First Incompleteness

Nyaya (7,966 words) [view diff] no match in snippet view article find links to article

objects, and their system of categories accurately mirrors reality's structure. Nyaya philosophy emphasizes the importance of universals, qualities,

Geometry (10,101 words) [view diff] no match in snippet view article find links to article

geometry; presently a geometric space, or simply a space is a mathematical structure on which some geometry is defined. The earliest recorded beginnings of

Hypercomputation (3,369 words) [view diff] no match in snippet view article find links to article

(2002). "Fuzzy logic, continuity and effectiveness". Archive for Mathematical Logic. 41 (7): 643–667. CiteSeerX 10.1.1.2.8029. doi:10.1007/s001530100128

Joseph Kouneiher (901 words) [view diff] no match in snippet view article find links to article

mathematical physics, he introduced the cohomological aspect of the mathematical logic theories or what we call now cohomological logic. The aim of the program

Word problem for groups (4,932 words) [view diff] no match in snippet view article find links to article

of the first examples of an unsolvable problem to be found not in mathematical logic or the theory of algorithms, but in one of the central branches of

Matroid (8,774 words) [view diff] no match in snippet view article find links to article

Finitary infinite matroids are studied in model theory, a branch of mathematical logic with strong ties to algebra. In the late 1960s matroid theorists asked

Hilary Putnam (8,923 words) [view diff] no match in snippet view article find links to article

next year, he was selected as Walter Beverly Pearson Professor of Mathematical Logic in recognition of his contributions to the philosophy of logic and

Computer science (6,712 words) [view diff] no match in snippet view article find links to article

useful interchange of ideas between the two fields in areas such as mathematical logic, category theory, domain theory, and algebra. The relationship between

Critical thinking (6,790 words) [view diff] no match in snippet view article find links to article

are induction and abduction. Deduction is the conclusion drawn from the structure of an argument's premises, by use of rules of inference formally those

Lenore Blum (1,740 words) [view diff] no match in snippet view article find links to article

Approach, showed deep connections between model theory (a branch of mathematical logic) and differential algebra. She was supervised by Gerald Sacks (after

Elementary mathematics (2,411 words) [view diff] no match in snippet view article find links to article

ISBN 978-0-17-658255-5. Rautenberg, Wolfgang (2010), A Concise Introduction to Mathematical Logic (3rd ed.), New York, NY: Springer Science+Business Media, doi:10

Semiotics (11,087 words) [view diff] no match in snippet view article find links to article

Maria Bochenski surveyed the field in this way: "Closely related to mathematical logic is the so-called semiotics (Charles Morris) which is now commonly

Martin Wirsing (1,190 words) [view diff] no match in snippet view article find links to article

he received his PhD from LMU in 1976, with a thesis on a topic in mathematical logic (Das Entscheidungsproblem der Prädikatenlogik mit Identität und Funktionszeichen)

Sense of smell (7,527 words) [view diff] no match in snippet view article find links to article

wrote that the study's "extravagant claims are based on errors of mathematical logic." The logic of his paper has in turn been criticized by the authors

Algebraic geometry (7,498 words) [view diff] no match in snippet view article find links to article

not working with kn is to emphasize that one "forgets" the vector space structure that kn carries. A function f : An → A1 is said to be polynomial (or regular)

Aaron Sloman (1,334 words) [view diff] no match in snippet view article find links to article

he became interested in philosophy after a brief period studying mathematical logic supervised by Hao Wang, eventually writing a DPhil in philosophy,

Science and technology in Russia (3,837 words) [view diff] no match in snippet view article find links to article

contributions to broadest range of mathematical branches, such as turbulence, mathematical logic, topology, differential equations, set theory, automata theory, information

Philomathean Society (3,389 words) [view diff] no match in snippet view article find links to article

philosopher, Walter Beverly Pearson Professor of Modern Mathematics and Mathematical Logic at Harvard University, and past president of the American Philosophical

Argument technology (2,483 words) [view diff] no match in snippet view article find links to article

ethics systems and moral reasoning components. In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool

Aaron Sloman (1,334 words) [view diff] no match in snippet view article find links to article

he became interested in philosophy after a brief period studying mathematical logic supervised by Hao Wang, eventually writing a DPhil in philosophy,

Prize of the Foundation for Polish Science (342 words) [view diff] no match in snippet view article find links to article

Ludomir Newelski University of Wrocław for his work in the field of mathematical logic, being a breakthrough in model theory and algebra 2002 Andrzej Udalski

Philomathean Society (3,389 words) [view diff] no match in snippet view article find links to article

philosopher, Walter Beverly Pearson Professor of Modern Mathematics and Mathematical Logic at Harvard University, and past president of the American Philosophical

Deductive reasoning (8,482 words) [view diff] no match in snippet view article find links to article

syllogism Logic and rationality Logical consequence Logical reasoning Mathematical logic Natural deduction Peirce's theory of deductive reasoning Propositional

Philosophy (17,451 words) [view diff] no match in snippet view article find links to article

original on 8 October 2020. Retrieved 22 February 2022. Li, Wei (2014). Mathematical Logic: Foundations for Information Science. Springer. ISBN 978-3-0348-0862-0

Juan David García Bacca (4,544 words) [view diff] no match in snippet view article find links to article

on the logical-genetic structure of the physical sciences. As a member of the Vienna Circle (1934-6) he taught mathematical logic and philosophy of science

Euler diagram (3,634 words) [view diff] no match in snippet view article find links to article

van Heijenoort, editor 1967 From Frege to Gödel: A Source Book of Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, MA, ISBN 0-674-32449-8

List of women in mathematics (23,282 words) [view diff] no match in snippet view article find links to article

Véronique Cortier, French mathematician and computer scientist, uses mathematical logic to verify cryptographic protocols Carla Cotwright-Williams (born 1973)

Presburger arithmetic (3,249 words) [view diff] no match in snippet view article find links to article

251–277. doi:10.1016/0168-0072(95)00022-4. Monk, J. Donald (2012). Mathematical Logic (Graduate Texts in Mathematics (37)) (Softcover reprint of the original

Constructive analysis (4,959 words) [view diff] no match in snippet view article find links to article

Palmgren, An Intuitionistic Axiomatisation of Real Closed Fields, Mathematical Logic Quarterly, Volume 48, Issue 2, Pages: 163-320, February 2002 Bridges

George Boole (7,414 words) [view diff] no match in snippet view article find links to article

Kolmogorov, Adolf Pavlovich Yushkevich, Mathematics of the 19th century: mathematical logic, algebra, number theory, probability theory (2001), pp. 15 (note 15)–16;

20th century in science (9,744 words) [view diff] no match in snippet view article find links to article

proved within the system. Hence mathematics cannot be reduced to mathematical logic, and David Hilbert's dream of making all of mathematics complete and

Arithmetic (16,396 words) [view diff] no match in snippet view article find links to article

ISBN 978-3-319-63624-5. O'Leary, Michael L. (2015). A First Course in Mathematical Logic and Set Theory. John Wiley & Sons. ISBN 978-0-470-90588-3. O'Regan

Axiom of regularity (2,938 words) [view diff] no match in snippet view article find links to article

van Heijenoort, Jean (1967). From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. pp. 393–413. von Neumann, John (1928). "Über die Definition

Characteristica universalis (4,792 words) [view diff] no match in snippet view article find links to article

Symbolic Logic 19: 133. Rogers, Jr., Hartley, 1963. "An Example in Mathematical Logic," The American Mathematical Monthly 70: 929–45. Rutherford, Donald

Indescribable cardinal (1,900 words) [view diff] no match in snippet view article find links to article

doi:10.1007/s11856-015-1191-7. W. N. Reinhardt, "Ackermann's set theory equals ZF", pp.234--235. Annals of Mathematical Logic vol. 2, iss. 2 (1970).

Alexander Grothendieck (8,661 words) [view diff] no match in snippet view article find links to article

of point-set topology, has influenced the fields of set theory and mathematical logic. The Weil conjectures were formulated in the later 1940s as a set

Conway's Game of Life (6,408 words) [view diff] no match in snippet view article find links to article

called a von Neumann universal constructor. Motivated by questions in mathematical logic and in part by work on simulation games by Ulam, among others, John

Penrose–Lucas argument (2,476 words) [view diff] no match in snippet view article find links to article

of natural numbers. See Mendelson, Elliot (2009). Introduction to Mathematical Logic (hardcover). Discrete Mathematics and Its Applications (5th ed.).

Pāṇini (6,085 words) [view diff] no match in snippet view article find links to article

century innovations of Gottlob Frege and the subsequent development of mathematical logic. In designing his grammar, Pāṇini used the method of "auxiliary symbols"

Luigi Moretti (3,102 words) [view diff] no match in snippet view article find links to article

architecture that was rigorous in the definition of form through the help of mathematical logic, computer techniques, and methods of operation research, and which

Ray tracing (graphics) (7,805 words) [view diff] no match in snippet view article

could be entering or exiting a material. Turner Whitted extended the mathematical logic for rays passing through a transparent solid to include the effects

List of University of Chicago faculty (4,756 words) [view diff] no match in snippet view article find links to article

Fields Medal and Wolf Prize winner Robert Soare – known for work in mathematical logic Norman Steenrod – topologist Marshall Stone – contributed to real

A New Kind of Science (3,449 words) [view diff] no match in snippet view article find links to article

also been criticized for being contrary to the spirit of research in mathematical logic and computational complexity theory, which seek to make fine-grained

Semantics (14,282 words) [view diff] no match in snippet view article find links to article

detailed analysis of how the English language can be represented using mathematical logic. It relies on higher-order logic, lambda calculus, and type theory

Aristotle (16,305 words) [view diff] no match in snippet view article find links to article

the dominant form of Western logic until 19th-century advances in mathematical logic. Kant stated in the Critique of Pure Reason that with Aristotle, logic

List of numeral systems (2,003 words) [view diff] no match in snippet view article find links to article

alongside the Middle Formative Mesoamerican scripts, the quinary-vigesimal structure of the system, and the general increase in the frequency and complexity

Computational law (4,406 words) [view diff] no match in snippet view article find links to article

communication and information theory to legal expression, the use of mathematical logic in law, the retrieval of legal data by electronic and mechanical means

Intuitionistic type theory (4,695 words) [view diff] no match in snippet view article find links to article

that exist. In the standard foundation, set theory combined with mathematical logic, the fundamental object is the set, which is a container that contains

Calculus (8,785 words) [view diff] no match in snippet view article find links to article

Robinson's approach, developed in the 1960s, uses technical machinery from mathematical logic to augment the real number system with infinitesimal and infinite

Reason (11,626 words) [view diff] no match in snippet view article find links to article

fallacy. Formal fallacies occur when there is a problem with the form, or structure, of the argument. The word "formal" refers to this link to the form of

Vector logic (3,789 words) [view diff] no match in snippet view article find links to article

Bern, Peter Lang. Mizraji, E. (1996) The operators of vector logic. Mathematical Logic Quarterly, 42, 27–39 Suppes, P. (1957) Introduction to Logic, Van

History of artificial intelligence (20,237 words) [view diff] no match in snippet view article find links to article

that would become the guiding faith of AI research. The study of mathematical logic provided the essential breakthrough that made artificial intelligence

Humanities (7,205 words) [view diff] no match in snippet view article find links to article

of reasoning, conceptual analysis, and the use of symbolic and/or mathematical logic, as contrasted with the Continental style of philosophy. This method

Glossary of artificial intelligence (29,481 words) [view diff] no match in snippet view article find links to article

decision theory. automated reasoning An area of computer science and mathematical logic dedicated to understanding different aspects of reasoning. The study

Inductive reasoning (8,642 words) [view diff] no match in snippet view article find links to article

minute and many-varied observations that uncovered the natural world's structure and causal relations needed to be coupled with enumerative induction in

Bracket (5,755 words) [view diff] no match in snippet view article find links to article

ceiling functions. The Quine corners ⌜ and ⌝ have at least two uses in mathematical logic: either as quasi-quotation, a generalization of quotation marks, or

Ordinal number (6,703 words) [view diff] no match in snippet view article find links to article

Jean van Heijenoort (ed.), From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 (3rd ed.), Harvard University Press, pp. 346–354, ISBN 0-674-32449-8

Existence (13,415 words) [view diff] no match in snippet view article find links to article

(1986). "The Method of Trigonometric Sums in Number Theory". Algebra, Mathematical Logic, Number Theory, Topology. American Mathematical Society. ISBN 978-0-8218-3096-3

Vedas (13,614 words) [view diff] no match in snippet view article find links to article

rediscovered again until the 1950s and the applications of modern mathematical logic to linguistics by Noam Chomsky. (Chomsky himself has said that the

Matrix (mathematics) (13,899 words) [view diff] no match in snippet view article

word "matrix" synonymously with the notion of truth table as used in mathematical logic. Mathematics portal List of named matrices Gram–Schmidt process –

Fundamental polygon (6,002 words) [view diff] no match in snippet view article find links to article

Yukshkevich, A. P., eds. (2001), Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory, Probability Theory, Springer, ISBN 978-3-7643-6441-0

Fixed-point combinator (5,183 words) [view diff] no match in snippet view article find links to article

expression to represent zero, or even many values. This is inconsistent in mathematical logic. An example implementation of Y in the language R is presented below:

Jesús Mosterín (4,526 words) [view diff] no match in snippet view article find links to article

international academies. He has played a crucial role in the introduction of mathematical logic, analytical philosophy and philosophy of science in Spain and Latin

List of multiple discoveries (11,338 words) [view diff] no match in snippet view article find links to article

1930: Undefinability theorem, an important limitative result in mathematical logic – Kurt Gödel (1930; described in a 1931 private letter, but not published);

List of Guggenheim Fellowships awarded in 1942 (1,072 words) [view diff] no match in snippet view article find links to article

geological structure underlying the North American Atlantic coastal plain Also won in 1941 Mathematics John Charles McKinsey New York University Mathematical logic

List of programming languages by type (6,703 words) [view diff] no match in snippet view article find links to article

(formulates data and the program evaluation mechanism as a special form of mathematical logic called Horn logic and a general proving mechanism called logical resolution)