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searching for Forcing (computability) 327 found (330 total)

alternate case: forcing (computability)

Computable set (500 words) [view diff] no match in snippet view article find links to article

In computability theory, a set of natural numbers is computable (or decidable or recursive) if there is an algorithm that computes the membership of every
Joel David Hamkins (1,791 words) [view diff] no match in snippet view article find links to article
theory (particularly the idea of the set-theoretic multiverse), in computability theory, and in group theory. After earning a Bachelor of Science in
List of statements independent of ZFC (2,182 words) [view diff] no match in snippet view article find links to article
CH cannot be disproven in ZFC; Paul Cohen later invented the method of forcing to exhibit a model of ZFC in which CH fails, showing that CH cannot be
Decision problem (1,246 words) [view diff] no match in snippet view article find links to article
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a
Mathematical logic (8,373 words) [view diff] no match in snippet view article find links to article
theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical
List of mathematical logic topics (1,012 words) [view diff] no match in snippet view article find links to article
syllogistic logic, see the list of topics in logic. See also the list of computability and complexity topics for more theory of algorithms. Peano axioms Giuseppe
Low basis theorem (570 words) [view diff] no match in snippet view article find links to article
The low basis theorem is one of several basis theorems in computability theory, each of which show that, given an infinite subtree of the binary tree
Undecidable problem (1,924 words) [view diff] no match in snippet view article find links to article
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct
Computable function (3,362 words) [view diff] no match in snippet view article find links to article
Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes
Computability theory (6,414 words) [view diff] no match in snippet view article find links to article
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated
Computably enumerable set (1,318 words) [view diff] no match in snippet view article find links to article
In computability theory, a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable
Formal language (3,163 words) [view diff] no match in snippet view article find links to article
expensive). Therefore, formal language theory is a major application area of computability theory and complexity theory. Formal languages may be classified in
Decidability (logic) (1,887 words) [view diff] no match in snippet view article
This is closely related to the concept of a many-one reduction in computability theory. A property of a theory or logical system weaker than decidability
Timeline of mathematical logic (948 words) [view diff] no match in snippet view article find links to article
presents "Turing's Thesis", asserting the identity of computability in general with computability by Turing machines, as an equivalent form of Church's
Enumeration (1,633 words) [view diff] no match in snippet view article find links to article
onto S need not imply the existence of an injection from S into I. In computability theory one often considers countable enumerations with the added requirement
Church–Turing thesis (6,849 words) [view diff] no match in snippet view article find links to article
In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's
Halting problem (7,350 words) [view diff] no match in snippet view article find links to article
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether
List of formal systems (284 words) [view diff] no match in snippet view article find links to article
Formal system – Mathematical model for deduction or proof systems Computability:Formal models Model of computation – Mathematical model describing how
Robert I. Soare (171 words) [view diff] no match in snippet view article find links to article
has done other work in mathematical logic, primarily in the area of computability theory. His doctoral students at the University of Chicago have included
Slicing the Truth (768 words) [view diff] no match in snippet view article find links to article
also review some of the tools needed in this study, including computability theory, forcing, and the low basis theorem. Chapter six, "the real heart of
Entscheidungsproblem (2,642 words) [view diff] no match in snippet view article find links to article
history leading to, and a discussion of, his proof. Soare, Robert I., "Computability and recursion", Bull. Symbolic Logic 2 (1996), no. 3, 284–321. Toulmin
Turing machine (9,386 words) [view diff] no match in snippet view article find links to article
of Turing machines has yielded many insights into computer science, computability theory, and complexity theory. In his 1948 essay, "Intelligent Machinery"
Primitive recursive function (7,342 words) [view diff] no match in snippet view article find links to article
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all
Generic filter (341 words) [view diff] no match in snippet view article find links to article
examplesPages displaying short descriptions of redirect targets in computability Rasiowa–Sikorski lemma – Mathematical lemma K. Ciesielski (1997). Set
Lindström's theorem (386 words) [view diff] no match in snippet view article find links to article
first course in logic: an introduction to model theory, proof theory, computability, and complexity, Oxford University Press, 2004, ISBN 0-19-852981-3,
Course-of-values recursion (1,299 words) [view diff] no match in snippet view article find links to article
In computability theory, course-of-values recursion is a technique for defining number-theoretic functions by recursion. In a definition of a function
Elementary diagram (182 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Strength (mathematical logic) (83 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Non-standard model (105 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Reverse mathematics (4,782 words) [view diff] no match in snippet view article find links to article
establish a close link between the complexity of a formula and the (non)computability of the set it defines. Another effect of using second-order arithmetic
Abstract logic (143 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Martin's axiom (806 words) [view diff] no match in snippet view article find links to article
Rasiowa–Sikorski lemma. It is a principle that is used to control certain forcing arguments. For a cardinal number κ, define the following statement: MA(κ)
Elementary function arithmetic (875 words) [view diff] no match in snippet view article find links to article
kind of mathematical function Grzegorczyk hierarchy – Functions in computability theory Reverse mathematics – Branch of mathematical logic Ordinal analysis –
Truth predicate (230 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Diagram (mathematical logic) (314 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Kolmogorov complexity (7,896 words) [view diff] no match in snippet view article find links to article
14words". It is also possible to show the non-computability of K by reduction from the non-computability of the halting problem H, since K and H are Turing-equivalent
Hereditary set (279 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Model complete theory (557 words) [view diff] no match in snippet view article find links to article
Wheeler, William H. (1975). "Model-completions and model-companions". Forcing, Arithmetic, Division Rings. Lecture Notes in Mathematics. Vol. 454. Springer
Lambda calculus (12,168 words) [view diff] no match in snippet view article find links to article
computable by any model of computation that is Turing complete. In fact computability can itself be defined via the lambda calculus: a function F: N → N of
Equiconsistency (732 words) [view diff] no match in snippet view article find links to article
is ZFC or an extension of it, the notion is meaningful. The method of forcing allows one to show that the theories ZFC, ZFC+CH and ZFC+¬CH are all equiconsistent
Axiom of global choice (458 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
James Earl Baumgartner (471 words) [view diff] no match in snippet view article find links to article
and Jaakko Hintikka, editors, Logic, Foundations of Mathematics and Computability Theory, pages 87–106. Reidel, 1977 Baumgartner, James E.; Galvin, Fred
Propositional variable (442 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Soundness (1,098 words) [view diff] no match in snippet view article find links to article
Macmillan Publishing Co., ISBN 0-02-324880-7 Boolos, Burgess, Jeffrey. Computability and Logic, 4th Ed, Cambridge, 2002. Wiktionary has definitions related
Axiom schema (470 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Formation rule (442 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Infinite set (917 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Quantifier rank (516 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
General set theory (1,235 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Lemma (mathematics) (399 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Extensionality (618 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Uncountable set (884 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Element (mathematics) (1,031 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Classical logic (841 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Fallibilism (2,886 words) [view diff] no match in snippet view article find links to article
hypothesis. The second type of undecidability is used in relation to computability theory (or recursion theory) and applies not solely to statements but
Predicate variable (560 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Transfinite induction (1,142 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Reduct (264 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Rasiowa–Sikorski lemma (424 words) [view diff] no match in snippet view article find links to article
one of the most fundamental facts used in the technique of forcing. In the area of forcing, a subset E of a poset (P, ≤) is called dense in P if for any
Independence (mathematical logic) (519 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Logical constant (289 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Atomic formula (523 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Tarski–Grothendieck set theory (1,135 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Axiom of adjunction (480 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Transitive set (1,222 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Symbol (formal) (494 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Sentence (mathematical logic) (458 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Truth value (862 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Urelement (995 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
T-schema (584 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Map (mathematics) (708 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Robinson arithmetic (1,839 words) [view diff] no match in snippet view article find links to article
JSTOR 2272251. Boolos, George; Burgess, John P.; Jeffrey, Richard (2002). Computability and Logic (4th ed.). Cambridge University Press. ISBN 0-521-00758-5
Uninterpreted function (410 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Cantor's paradox (734 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Well-formed formula (2,164 words) [view diff] no match in snippet view article find links to article
(1): 29–41 Boolos, George; Burgess, John; Jeffrey, Richard (2002), Computability and Logic (4th ed.), Cambridge University Press, ISBN 978-0-521-00758-0
Universal set (1,327 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Predicate (logic) (421 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Free logic (973 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Formal proof (579 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Continuum hypothesis (4,060 words) [view diff] no match in snippet view article find links to article
independence proof. To prove his result, Cohen developed the method of forcing, which has become a standard tool in set theory. Essentially, this method
Ground expression (656 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Compactness theorem (1,931 words) [view diff] no match in snippet view article find links to article
Hodges (1993). Boolos, George; Jeffrey, Richard; Burgess, John (2004). Computability and Logic (fourth ed.). Cambridge University Press. Chang, C.C.; Keisler
Foundations of mathematics (6,910 words) [view diff] no match in snippet view article find links to article
mathematical logic that includes set theory, model theory, proof theory, computability and computational complexity theory, and more recently, parts of computer
Gödel numbering (1,536 words) [view diff] no match in snippet view article find links to article
about the consistency and completeness properties of formal systems. In computability theory, the term "Gödel numbering" is used in settings more general
Abstract model theory (169 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Logical equivalence (751 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Non-standard model of arithmetic (1,292 words) [view diff] no match in snippet view article find links to article
countable dense linear order. Boolos, George, and Jeffrey, Richard 1974. Computability and Logic, Cambridge University Press. ISBN 0-521-38923-2. Skolem, Thoralf
Uniqueness quantification (848 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Monadic predicate calculus (698 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Intersection (set theory) (1,734 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Spectrum of a sentence (1,365 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Satisfiability (1,500 words) [view diff] no match in snippet view article find links to article
(MIT Press). Boolos, George; Burgess, John; Jeffrey, Richard (2007). Computability and Logic (5th ed.). Cambridge University Press. Daniel Kroening; Ofer
Semantic theory of truth (1,050 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Substructure (mathematics) (754 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Class (set theory) (1,279 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Self-verifying theories (419 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Axiom of constructibility (1,064 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Kripke–Platek set theory (1,586 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Complete theory (396 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Spectrum of a theory (1,132 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Gödel's incompleteness theorems (12,165 words) [view diff] no match in snippet view article find links to article
second sense, which will not be discussed here, is used in relation to computability theory and applies not to statements but to decision problems, which
Semantics of logic (707 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Saturated model (1,096 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Tarski's undefinability theorem (2,271 words) [view diff] no match in snippet view article find links to article
Logic. North-Holland. Boolos, G.; Burgess, J.; Jeffrey, R. (2002). Computability and Logic (4th ed.). Cambridge University Press. Lucas, J. R. (1961)
Axiom of dependent choice (950 words) [view diff] no match in snippet view article find links to article
converse is proved in Boolos, George S.; Jeffrey, Richard C. (1989). Computability and Logic (3rd ed.). Cambridge University Press. pp. 155–156. ISBN 0-521-38026-X
Aczel's anti-foundation axiom (273 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Higher-order logic (1,066 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Apartness relation (646 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Arity (1,464 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Union (set theory) (1,967 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Large cardinal (1,333 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Domain of a function (962 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Validity (logic) (1,110 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Complement (set theory) (1,515 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Set theory (6,586 words) [view diff] no match in snippet view article find links to article
of forcing while searching for a model of ZFC in which the continuum hypothesis fails, or a model of ZF in which the axiom of choice fails. Forcing adjoins
C-minimal theory (421 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Mathematical structure (650 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Signature (logic) (1,339 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Extension by new constant and function names (425 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Alphabet (formal languages) (843 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Empty set (2,229 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Mostowski collapse lemma (591 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Subset (1,734 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Monadic second-order logic (1,308 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Open formula (394 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Robinson's joint consistency theorem (321 words) [view diff] no match in snippet view article find links to article
test Boolos, George S.; Burgess, John P.; Jeffrey, Richard C. (2002). Computability and Logic. Cambridge University Press. p. 264. ISBN 0-521-00758-5. Robinson
Completeness (logic) (771 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Non-logical symbol (783 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Aleph number (2,453 words) [view diff] no match in snippet view article find links to article
the CH itself is not a theorem of ZFC – by the (then-novel) method of forcing. Aleph-omega is ℵ ω = sup { ℵ n | n ∈ ω } = sup { ℵ n | n ∈ { 0 , 1 , 2
Setoid (532 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Logical equality (614 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Codomain (1,051 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Diagonal intersection (386 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Inhabited set (1,358 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Atomic model (mathematical logic) (344 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Range of a function (830 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Syntax (logic) (1,052 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Łoś–Vaught test (235 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Elementary equivalence (956 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Power set (2,479 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
List of mathematical proofs (593 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Beth definability (315 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
History of logic (13,255 words) [view diff] no match in snippet view article find links to article
research: model theory, proof theory, computability theory, and set theory. In set theory, the method of forcing revolutionized the field by providing
Extension by definition (1,506 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Argument of a function (440 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Binary operation (1,546 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Metavariable (329 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Existential quantification (1,535 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Finite-valued logic (1,322 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Categorical theory (1,157 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Metavariable (329 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Prime model (508 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Zermelo–Fraenkel set theory (6,282 words) [view diff] no match in snippet view article find links to article
Since forcing preserves choice, we cannot directly produce a model contradicting choice from a model satisfying choice. However, we can use forcing to create
Infinite-valued logic (1,479 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Institutional model theory (358 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Elementary proof (623 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Finite set (2,594 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Primitive recursive arithmetic (1,378 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Non-well-founded set theory (1,479 words) [view diff] no match in snippet view article find links to article
Mathématique de Belgique, 20: 3–15, Zbl 0179.01602 Boffa, M. (1972), "Forcing et négation de l'axiome de Fondement", Acad. Roy. Belgique, Mém. Cl. Sci
Stratification (mathematics) (820 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Functional predicate (1,254 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Saturated set (1,160 words) [view diff] no match in snippet view article find links to article
\varnothing } or to f − 1 ( y ) . {\displaystyle f^{-1}(y).} Related to computability theory, this notion can be extended to programs. Here, considering a
Grothendieck universe (1,342 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Von Neumann cardinal assignment (651 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Fodor's lemma (475 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Automated theorem proving (2,933 words) [view diff] no match in snippet view article find links to article
on the one hand gave two independent but equivalent definitions of computability, and on the other gave concrete examples of undecidable questions. In
Proof without words (931 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Paradoxes of set theory (2,657 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Conservative extension (888 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Metalanguage (1,418 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Weakly o-minimal structure (508 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Logical conjunction (1,465 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Axiomatic system (1,765 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Logical truth (1,094 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Peano axioms (6,478 words) [view diff] no match in snippet view article find links to article
Kaye 1991, Section 11.3. Kaye 1991, pp. 70ff.. Davis, Martin (1974). Computability. Notes by Barry Jacobs. Courant Institute of Mathematical Sciences,
Richard's paradox (1,800 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Atomic sentence (1,196 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Finitary relation (1,905 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Von Neumann universe (2,818 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Theorem (4,409 words) [view diff] no match in snippet view article find links to article
1994, p. 104. Boolos, George; Burgess, John; Jeffrey, Richard (2007). Computability and Logic (5th ed.). Cambridge University Press. Enderton, Herbert (2001)
Richardson's theorem (701 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Tarski's theorem about choice (583 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Theory (mathematical logic) (1,695 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Surjective function (1,941 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Algebra of sets (1,865 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Formal system (1,544 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Logical consequence (1,910 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Injective function (2,589 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Bijection (2,508 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Ordered pair (3,697 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Type (model theory) (2,253 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Hilbert's second problem (1,500 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Regular cardinal (1,437 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Back-and-forth method (688 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Amalgamation property (817 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Interpretation (model theory) (824 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Proof by exhaustion (940 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Proof by exhaustion (940 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Cardinal number (3,834 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
O-minimal theory (1,294 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Hilbert's axioms (2,313 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Schröder–Bernstein theorem (2,374 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Model-theoretic grammar (526 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Contradiction (2,673 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Identity type (406 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Negation (2,236 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Extender (set theory) (701 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Countable set (4,381 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Mathematical object (2,769 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Expression (mathematics) (5,319 words) [view diff] no match in snippet view article
Norton & Company. ISBN 978-0-393-04785-1. Davis, Martin (1982-01-01). Computability & Unsolvability. Courier Corporation. ISBN 978-0-486-61471-7. Turing
Universal quantification (2,503 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Cartesian product (3,944 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Transfer principle (2,686 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Morse–Kelley set theory (3,186 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Logical disjunction (1,937 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Supertask (2,391 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Axiom (4,918 words) [view diff] no match in snippet view article find links to article
Zermelo–Fraenkel axioms for set theory. Furthermore, using techniques of forcing (Cohen) one can show that the continuum hypothesis (Cantor) is independent
Well-founded relation (1,378 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Gödel's completeness theorem (2,330 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Universe (mathematics) (2,649 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Cantor's diagonal argument (2,808 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Substitution (logic) (2,938 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Cantor's theorem (3,735 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Material conditional (2,229 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Algebraic logic (2,220 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Mathematical and theoretical biology (4,322 words) [view diff] no match in snippet view article find links to article
 1513–1577. Lin HC (2004). "Computer Simulations and the Question of Computability of Biological Systems" (PDF). Computer Models and Automata Theory in
Computer-assisted proof (2,059 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Ada Lovelace (9,797 words) [view diff] no match in snippet view article find links to article
Computability". Ada Lovelace Day. FindingAda.com. 31 January 2016. Retrieved 11 January 2016. "The Ada Lovelace Bicentenary Lectures on Computability"
Joint embedding property (320 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Naive set theory (4,782 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Equivalence relation (4,473 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Boolean function (2,887 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Set (mathematics) (7,143 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Recursion (3,669 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Strongly minimal theory (405 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Successor cardinal (564 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
List of first-order theories (5,269 words) [view diff] no match in snippet view article find links to article
hypothesis), Martin's maximum ◊ and ♣ Axiom of constructibility (V=L) Proper forcing axiom Analytic determinacy, projective determinacy, Axiom of determinacy
NP (complexity) (2,784 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Ultraproduct (3,087 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Square of opposition (3,161 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Inaccessible cardinal (2,405 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Term (logic) (2,808 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Proof by contradiction (2,602 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Consistency (2,931 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Ross–Littlewood paradox (1,264 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Russell's paradox (4,621 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Axiom of choice (7,923 words) [view diff] no match in snippet view article find links to article
ZF itself is consistent. In 1963, Paul Cohen employed the technique of forcing, developed for this purpose, to show that, assuming ZF is consistent, the
Russell's paradox (4,621 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Finite model theory (3,093 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Logical connective (3,164 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Functional completeness (1,957 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Formal grammar (3,450 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Löwenheim–Skolem theorem (2,795 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Decidability of first-order theories of the real numbers (503 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Kőnig's theorem (set theory) (1,232 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Fraïssé limit (1,388 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Variable (mathematics) (3,793 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Tarski's axioms (3,825 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Gentzen's consistency proof (1,993 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Venn diagram (3,242 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Cardinal assignment (589 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Structural induction (1,750 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Term logic (3,903 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Skolem's paradox (3,331 words) [view diff] no match in snippet view article find links to article
the study of set theory. Paul Cohen's method for extending set theory, forcing, is often explained in terms of countable models, and was described by
List of axiomatic systems in logic (3,906 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Three-valued logic (3,292 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Logical biconditional (1,794 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Constructible universe (6,103 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Constructive set theory (35,229 words) [view diff] no match in snippet view article find links to article
standard axioms to classically equivalent ones. Apart from demands for computability and reservations regrading of impredicativity, technical question regarding
Law of noncontradiction (3,139 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
List of superseded scientific theories (3,004 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Mathematical proof (4,229 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Feferman–Vaught theorem (1,233 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Truth table (3,307 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Fixed-point logic (2,031 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Argument (4,260 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Unbounded nondeterminism (2,718 words) [view diff] no match in snippet view article find links to article
could theoretically solve the halting problem, a famous challenge in computability theory that asks whether a Turing machine will stop or continue forever
Club filter (754 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Quantifier (logic) (4,501 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Kurt Gödel (5,947 words) [view diff] no match in snippet view article find links to article
Mathematical Society. During this year, Gödel also developed the ideas of computability and recursive functions to the point where he was able to present a
Second-order logic (4,502 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Interpretation (logic) (4,478 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Proof of impossibility (3,915 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Philosophy of mathematics (10,555 words) [view diff] no match in snippet view article find links to article
advocated by mathematical intuitionists and constructivists in the "computability" tradition—. The French mathematician Henri Poincaré was among the first
Truth-value semantics (632 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Proof by infinite descent (2,223 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Zorn's lemma (4,665 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Syllogism (5,135 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Induction, bounding and least number principles (1,211 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Rule of inference (7,327 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
New Foundations (8,162 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Determinacy (4,125 words) [view diff] no match in snippet view article find links to article
1142/9789812564894_0005. ISBN 978-981-02-4736-2. Soare, Robert I. (2016). Turing Computability: Theory and Applications. Springer. pp. 217ff. ISBN 978-3-6423-1932-7
Structure (mathematical logic) (5,140 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Model theory (9,064 words) [view diff] no match in snippet view article find links to article
Gödel's work on the constructible universe, which, along with the method of forcing developed by Paul Cohen can be shown to prove the (again philosophically
Law of excluded middle (5,601 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Cardinality (11,564 words) [view diff] no match in snippet view article find links to article
independent from ZFC. To prove his result, Cohen developed the method of forcing, which has become a standard tool in set theory. Essentially, this method
Von Neumann–Bernays–Gödel set theory (15,666 words) [view diff] no match in snippet view article find links to article
factors, including the extra work required to handle forcing in NBG, Cohen's 1966 presentation of forcing, which used ZF, and the proof that NBG is a conservative
Ultrafilter on a set (7,379 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Stable theory (3,633 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Principia Mathematica (9,478 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Type theory (8,230 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Proof sketch for Gödel's first incompleteness theorem (2,988 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Mathematical induction (6,914 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Timeline of mathematics (7,870 words) [view diff] no match in snippet view article find links to article
λ-calculus and the Turing machine, formalizing the notion of computation and computability. 1938 – Tadeusz Banachiewicz introduces LU decomposition. 1940 – Kurt
Equivalent definitions of mathematical structures (3,272 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Tarski's high school algebra problem (1,991 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Boolean algebra (9,571 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Contraposition (6,175 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Propositional formula (11,131 words) [view diff] no match in snippet view article find links to article
Library of Congress Catalog Card Number 67-12342. Useful especially for computability, plus good sources. Joel W. Robbin 1969, 1997, Mathematical Logic: A
Equality (mathematics) (7,795 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Satisfiability modulo theories (4,371 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Epsilon-induction (4,195 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Noam Chomsky (18,675 words) [view diff] no match in snippet view article find links to article
December 9, 2015. Davis, Martin; Weyuker, Elaine J.; Sigal, Ron (1994). Computability, complexity, and languages: fundamentals of theoretical computer science
Natural deduction (7,755 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Church encoding (8,556 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
First-order logic (12,955 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Propositional logic (11,449 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Logicism (11,833 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
History of mathematics (17,048 words) [view diff] no match in snippet view article find links to article
areas of mathematics were developed to deal with this: Alan Turing's computability theory; complexity theory; Derrick Henry Lehmer's use of ENIAC to further
Turing's proof (7,140 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
List of women in mathematics (23,412 words) [view diff] no match in snippet view article find links to article
1957), Portuguese and Swiss stochastic analyst Barbara Csima, Canadian computability theorist, president of Canadian Mathematical Society Marianna Csörnyei
Cantor's first set theory article (7,563 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Conjunction/disjunction duality (1,337 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
List of set identities and relations (29,862 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Implementation of mathematics in set theory (10,960 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Glossary of logic (30,237 words) [view diff] no match in snippet view article find links to article
logical and linguistic intuitions. busy beaver problem A problem in computability theory that seeks the Turing machine with the largest possible behavior
Hilbert system (3,534 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable