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searching for Numbering (computability theory) 330 found (338 total)

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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
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
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
Index set (computability) (703 words) [view diff] no match in snippet view article
In computability theory, index sets describe classes of computable functions; specifically, they give all indices of functions in a certain class, according
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
UTM theorem (242 words) [view diff] no match in snippet view article find links to article
In computability theory, the UTM theorem, or universal Turing machine theorem, is a basic result about Gödel numberings of the set of computable functions
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
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 the
Kleene's recursion theorem (3,095 words) [view diff] no match in snippet view article find links to article
In computability theory, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions
Kleene's T predicate (1,207 words) [view diff] no match in snippet view article find links to article
In computability theory, the T predicate, first studied by mathematician Stephen Cole Kleene, is a particular set of triples of natural numbers that is
Computably inseparable (503 words) [view diff] no match in snippet view article find links to article
In computability theory, two disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated"
PA degree (864 words) [view diff] no match in snippet view article find links to article
In the mathematical field of computability theory, a PA degree is a Turing degree that computes a complete extension of Peano arithmetic (Jockusch 1987)
Theory of computation (2,168 words) [view diff] no match in snippet view article find links to article
into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question:
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
Creative and productive sets (1,306 words) [view diff] no match in snippet view article find links to article
In computability theory, productive sets and creative sets are types of sets of natural numbers that have important applications in mathematical logic
Gödel numbering for sequences (3,616 words) [view diff] no match in snippet view article find links to article
In mathematics, a Gödel numbering for sequences provides an effective way to represent each finite sequence of natural numbers as a single natural number
Turing jump (896 words) [view diff] no match in snippet view article find links to article
In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is an operation that assigns to each decision problem X a successively
Entscheidungsproblem (2,642 words) [view diff] no match in snippet view article find links to article
incompleteness theorem, especially by the method of assigning numbers (a Gödel numbering) to logical formulas in order to reduce logic to arithmetic. The Entscheidungsproblem
Computability (3,293 words) [view diff] no match in snippet view article find links to article
problem by an effective procedure. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer
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
Integer-valued function (412 words) [view diff] no match in snippet view article find links to article
functions on Nn. Gödel numbering, defined on well-formed formulae of some formal language, is a natural-valued function. Computability theory is essentially based
Enumeration reducibility (1,438 words) [view diff] no match in snippet view article find links to article
In computability theory, enumeration reducibility (or e-reducibility for short) is a specific type of reducibility. Roughly speaking, A is enumeration-reducible
List of statements independent of ZFC (2,182 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Smn theorem (1,202 words) [view diff] no match in snippet view article find links to article
In computability theory the S m n  theorem, written also as "smn-theorem" or "s-m-n theorem" (also called the translation lemma, parameter theorem, and
Elementary cellular automaton (2,819 words) [view diff] no match in snippet view article find links to article
In mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled
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
Rice's theorem (1,712 words) [view diff] no match in snippet view article find links to article
In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable. A semantic property is one about the
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
Specker sequence (697 words) [view diff] no match in snippet view article find links to article
In computability theory, a Specker sequence is a computable, monotonically increasing, bounded sequence of rational numbers whose supremum is not a computable
Elementary diagram (182 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Turing machine (9,386 words) [view diff] no match in snippet view article find links to article
Turing machines has yielded many insights into computer science, computability theory, and complexity theory. In his 1948 essay, "Intelligent Machinery"
Strength (mathematical logic) (83 words) [view diff] no match in snippet view article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Abstract logic (143 words) [view diff] no match in snippet view article find links to article
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
List of formal systems (284 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Hereditary set (279 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
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
Kolmogorov complexity (7,896 words) [view diff] no match in snippet view article find links to article
A must be true. This "formalization" can be achieved based on a Gödel numbering. Theorem: There exists a constant L (which only depends on S and on the
Propositional variable (442 words) [view diff] no match in snippet view article find links to article
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Enumeration (1,633 words) [view diff] no match in snippet view article find links to article
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
Quantifier rank (516 words) [view diff] no match in snippet view article find links to article
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Predicate variable (560 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Independence (mathematical logic) (519 words) [view diff] no match in snippet view article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Diagonal lemma (1,745 words) [view diff] no match in snippet view article find links to article
diagonal lemma is closely related to Kleene's recursion theorem in computability theory, and their respective proofs are similar. In 1952, Léon Henkin asked
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
Model complete theory (557 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Axiom of global choice (458 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Abstract model theory (169 words) [view diff] no match in snippet view article find links to article
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Lindström's theorem (386 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Equiconsistency (732 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Rice–Shapiro theorem (3,454 words) [view diff] no match in snippet view article find links to article
In computability theory, the Rice–Shapiro theorem is a generalization of Rice's theorem, named after Henry Gordon Rice and Norman Shapiro. It states that
Uninterpreted function (410 words) [view diff] no match in snippet view article find links to article
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Lambda calculus (12,168 words) [view diff] no match in snippet view article find links to article
calculus. Building on earlier work by Kleene and constructing a Gödel numbering for lambda expressions, he constructs a lambda expression e that closely
Timeline of mathematical logic (948 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Axiom schema (470 words) [view diff] no match in snippet view article find links to article
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Ground expression (656 words) [view diff] no match in snippet view article find links to article
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
C-minimal theory (421 words) [view diff] no match in snippet view article find links to article
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Uniqueness quantification (848 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Semantic theory of truth (1,050 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Semantics of logic (707 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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 subset
Signature (logic) (1,339 words) [view diff] no match in snippet view article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Completeness (logic) (771 words) [view diff] no match in snippet view article
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
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
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
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Robinson arithmetic (1,836 words) [view diff] no match in snippet view article find links to article
arithmetic to carry out the necessary coding constructions (of which Gödel numbering forms a part). The axioms of Q were chosen specifically to ensure they
Argument of a function (440 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Stratification (mathematics) (820 words) [view diff] no match in snippet view article
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Universal set (1,327 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Extension by definition (1,506 words) [view diff] no match in snippet view article find links to article
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
assigned a distinct number. This procedure is known variously as Gödel numbering, coding and, more generally, as arithmetization. In particular, various
Finite-valued logic (1,322 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Aczel's anti-foundation axiom (273 words) [view diff] no match in snippet view article find links to article
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Infinite-valued logic (1,479 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Proof without words (931 words) [view diff] no match in snippet view article find links to article
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
allows the formula to be effectively recovered from the number. This numbering is extended to cover finite sequences of formulas. In the second part
Diagonal intersection (386 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Condensation lemma (210 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Formal language (3,163 words) [view diff] no match in snippet view article find links to article
Therefore, formal language theory is a major application area of computability theory and complexity theory. Formal languages may be classified in the
Finite set (2,594 words) [view diff] no match in snippet view article find links to article
18 July 2023 This list of 8 finiteness concepts is presented with this numbering scheme by both Howard & Rubin 1998, pp. 278–280, and Lévy 1958, pp. 2–3
Identity type (406 words) [view diff] no match in snippet view article find links to article
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Richardson's theorem (701 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Grothendieck universe (1,342 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Setoid (532 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Richard's paradox (1,800 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Index of computing articles (1,384 words) [view diff] no match in snippet view article find links to article
logarithm – Common Unix Printing System – Compact disc – Compiler – Computability theory – Computational complexity theory – Computation – Computer-aided
Logical truth (1,094 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Joint embedding property (320 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Formal system (1,527 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Generic filter (341 words) [view diff] no match in snippet view article find links to article
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Proof theory (2,669 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Universal quantification (2,503 words) [view diff] no match in snippet view article find links to article
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Well-founded relation (1,378 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Negation (2,250 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Computer-assisted proof (2,059 words) [view diff] no match in snippet view article find links to article
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
there is a formal statement Con(ZFC) (one for each appropriate Gödel numbering scheme) expressing the consistency of ZFC, that is also independent of
Non-well-founded set theory (1,479 words) [view diff] no match in snippet view article find links to article
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
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
sense, which will not be discussed here, is used in relation to computability theory and applies not to statements but to decision problems, which are
Cardinal assignment (589 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Material conditional (2,194 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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
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
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
NP (complexity) (2,784 words) [view diff] no match in snippet view article
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
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
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
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
the moment) the parameters, the formulas can be given a standard Gödel numbering by the natural numbers. If Φ {\displaystyle \Phi } is the formula with
Constructible universe (6,103 words) [view diff] no match in snippet view article find links to article
the moment) the parameters, the formulas can be given a standard Gödel numbering by the natural numbers. If Φ {\displaystyle \Phi } is the formula with
Consistency (2,931 words) [view diff] no match in snippet view article find links to article
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Tautology (logic) (3,127 words) [view diff] no match in snippet view article
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
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
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
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
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Truth-value semantics (632 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
List of axiomatic systems in logic (3,906 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Theorem (4,452 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Law of noncontradiction (3,139 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
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
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Second-order logic (4,502 words) [view diff] no match in snippet view article find links to article
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Zorn's lemma (4,674 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Expression (mathematics) (5,336 words) [view diff] no match in snippet view article
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Club filter (754 words) [view diff] no match in snippet view article find links to article
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
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Equivalent definitions of mathematical structures (3,272 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Equivalent definitions of mathematical structures (3,272 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Law of excluded middle (5,601 words) [view diff] no match in snippet view article find links to article
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
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
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
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
must always be taken with insights about totality of functions. In computability theory, the μ operator enables all partial general recursive functions (or
Type theory (8,230 words) [view diff] no match in snippet view article find links to article
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
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
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
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
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
unexpected ideas had arisen and significant changes were coming. With Gödel numbering, propositions could be interpreted as referring to themselves or other
Principia Mathematica (9,478 words) [view diff] no match in snippet view article find links to article
3 was not reset, being photographically reprinted with the same page numbering; corrections were still made. The total number of pages (excluding the
Foundations of mathematics (6,910 words) [view diff] no match in snippet view article find links to article
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
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
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
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
in general – cannot. Tarski's undefinability theorem shows that Gödel numbering can be used to prove syntactical constructs, but not semantic assertions
Propositional formula (11,131 words) [view diff] no match in snippet view article find links to article
the number of literals. In the following table, observe the peculiar numbering of the rows: (0, 1, 3, 2, 6, 7, 5, 4, 0). The first column is the decimal
Model theory (9,064 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Equality (mathematics) (7,795 words) [view diff] no match in snippet view article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Ultrafilter on a set (7,379 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Natural deduction (7,755 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Cardinality (11,693 words) [view diff] no match in snippet view article find links to article
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
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Propositional logic (11,466 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Von Neumann–Bernays–Gödel set theory (15,666 words) [view diff] no match in snippet view article find links to article
bound variables are replaced by subscripted variables that continue the numbering of the free set variables. Since bound variables are free for part of
Turing's proof (7,140 words) [view diff] no match in snippet view article find links to article
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
Cantor's first set theory article (7,563 words) [view diff] no match in snippet view article find links to article
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
principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable
List of inventions and discoveries by women (7,761 words) [view diff] no match in snippet view article find links to article
Supercomputer Center. 1997. Retrieved 23 August 2017. S. Barry Cooper, Computability theory, p. 98 The adjective "optimum" (and not "optimal") "is the slightly
List of set identities and relations (29,862 words) [view diff] no match in snippet view article find links to article
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
educator Julia F. Knight, American specialist in model theory and computability theory Sarah Koch (born 1979), American complex analyst and complex dynamicist
Hilbert system (3,534 words) [view diff] no match in snippet view article find links to article
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