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Computability theory
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Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originatedDecision 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 aComputably 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 decidableIndex 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, accordingUndecidable 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 constructUTM 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 functionsComputable 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 everyHalting 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 theKleene'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 descriptionsKleene'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 isComputably 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 functionCreative 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 logicGödel 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 numberTuring 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 successivelyEntscheidungsproblem (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 EntscheidungsproblemComputability (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 computerComputable 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 computesInteger-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 basedEnumeration 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-reducibleList 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 ComputableSmn 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, andElementary 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 (labeledPrimitive 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 allRice'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 theChurch–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'sSpecker 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 computableElementary 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 ComputableTuring 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 ComputableAbstract 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 ComputableNon-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 ComputableReverse 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 ComputableList 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 ComputableElementary 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 ComputableDiagram (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 ComputableHereditary 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 ComputableMathematical 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 mathematicalKolmogorov 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 thePropositional 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 ComputableFormation 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 ComputableLemma (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 ComputableEnumeration (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 requirementQuantifier 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 ComputableReduct (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 ComputableExtensionality (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 ComputablePredicate 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 ComputableClassical 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 ComputableIndependence (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 ComputableDiagonal 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 askedDecidability (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 decidabilityModel 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 ComputableAxiom 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 ComputableAbstract 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 ComputableAtomic 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 ComputableLogical 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 ComputableLindström'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 ComputableEquiconsistency (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 ComputableT-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 ComputableRice–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 thatUninterpreted 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 ComputableSentence (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 ComputableUrelement (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 ComputableSymbol (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 ComputableLambda 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 closelyTimeline 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 ComputableAxiom 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 ComputableMap (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 ComputableTruth 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 ComputablePredicate (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 ComputableFree 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 ComputableGround 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 ComputableFormal 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 ComputableInfinite 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 ComputableLogical 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 ComputableC-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 ComputableGeneral 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 ComputableAtomic 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 ComputableUniqueness 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 ComputableSemantic 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 ComputableSpectrum 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 ComputableSelf-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 ComputableŁoś–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 ComputableMonadic 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 ComputableUncountable 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 ComputableSubstructure (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 ComputableComplete 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 ComputableSpectrum 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 ComputableTransfinite 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 ComputableSaturated 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 ComputableBeth 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 ComputableInstitutional 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 ComputablePrime 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 ComputableSemantics 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 ComputableAxiom 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 ComputableHigher-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 ComputableElement (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 ComputableList 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 ComputableMartin'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 ComputableSaturated 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 subsetSignature (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 ComputableMathematical 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 ComputableCompleteness (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 ComputableAlphabet (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 ComputableArity (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 ComputableRange 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 ComputableExtension 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 ComputableDomain 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 ComputableTarski–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 ComputableTransitive 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 ComputableMonadic 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 ComputableMetavariable (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 ComputableElementary 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 ComputableRobinson 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 theyArgument 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 ComputableOpen 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 ComputableValidity (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 ComputableCantor'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 ComputableNon-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 ComputableLogical 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 ComputableSoundness (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 ComputableInhabited 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 ComputableWeakly 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 ComputableCodomain (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 ComputableStratification (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 ComputableElementary 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 ComputableSyntax (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 ComputableUniversal 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 ComputableExtension 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 ComputableTarski'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, variousFinite-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 ComputableExistential 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 ComputableAczel'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 ComputableCategorical 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 ComputableApartness 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 ComputableInfinite-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 ComputablePrimitive 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 ComputableVon 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 ComputableBinary 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 ComputableBinary 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 ComputableMostowski 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 ComputableProof 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 ComputableProof 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 partDiagonal 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 ComputableCondensation 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 ComputableAxiom 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 ComputableFormal 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 theFinite 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. 2–3Identity 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 ComputableFunctional 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 ComputableKripke–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 ComputableRichardson'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 ComputableClass (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 ComputableGrothendieck 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 ComputableSetoid (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 ComputableIntersection (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 ComputableAmalgamation 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 ComputableModel-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 ComputableConservative 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 ComputableBack-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 ComputableInterpretation (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 ComputableMetalanguage (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 ComputableRichard'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 ComputableExtender (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 ComputableRasiowa–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 ComputableAtomic 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 ComputableLarge 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 ComputableComplement (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 ComputableUnion (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 ComputableLogical 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 ComputableHilbert'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 ComputableAxiomatic 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 ComputableIndex 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-aidedLogical 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 ComputableFodor'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 ComputableFinitary 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 ComputableTheory (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 ComputableO-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 ComputableCompactness 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 ComputableWell-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 ComputableJoint 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 ComputableProof 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 ComputableSubset (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 ComputableEmpty 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 ComputableNon-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 ComputableSurjective 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 ComputableType (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 ComputableRobinson'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 ComputablePower 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 ComputableLogical 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 ComputableFormal 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 ComputableGeneric 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 ComputableStrongly 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 ComputableTarski'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 ComputableInjective 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 ComputableProof 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 ComputableSatisfiability (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 ComputableUniversal 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 ComputableContradiction (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 ComputableMathematical 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 ComputableSuccessor 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 ComputableTransfer 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 ComputableWell-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 ComputableAlgebraic 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 ComputableNegation (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 ComputableSupertask (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 ComputableAleph 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 ComputableSubstitution (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 ComputableParadoxes 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 ComputableGödel'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 ComputableLogical 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 ComputableUniverse (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 ComputableComputer-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 ComputableContinuum 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 ofNon-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 ComputableDecidability 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 ComputableGödel'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 areCardinal 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 ComputableRoss–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 ComputableMaterial 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 ComputableBoolean 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 ComputableKőnig'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 ComputableRegular 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 ComputableVon 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 ComputableAlgebra 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 ComputableFraïssé 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 ComputableGentzen'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 ComputableFeferman–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 ComputableUltraproduct (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 ComputableInaccessible 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 ComputableRecursion (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 ComputableFunctional 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 ComputableProof 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 ComputableSquare 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 ComputableNP (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 ComputableFinite 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 ComputableTerm (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 ComputableBijection (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 ComputableConstructible 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 withConstructible 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 withConsistency (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 ComputableSchröder–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 ComputableStructural 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 ComputableTautology (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 ComputableLogical 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 ComputableLöwenheim–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 ComputableFixed-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 ComputableCardinal 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 ComputableInduction, 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 ComputableFormal 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 ComputableTarski'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 ComputableCartesian 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 ComputableAutomated 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 ComputableCountable 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 ComputableMorse–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 ComputableTruth-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 ComputableList 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 ComputableVariable (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 ComputableLogical 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 ComputableAxiom (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 ComputableThree-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 ComputableCantor'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 ComputableTerm 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 ComputableCantor'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 ComputableTheorem (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 ComputableLaw 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 ComputableEquivalence 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 ComputableNaive 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 ComputableList 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 ComputableProof 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 ComputableMathematical 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 ComputableTruth 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 ComputableSet (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 ComputableList 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 ComputableProof 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 ComputableSecond-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 ComputableInterpretation (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 ComputableQuantifier (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 ComputableArgument (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 ComputableZorn'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 ComputableExpression (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 ComputableSkolem'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 ComputableRussell'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 ComputableTarski'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 ComputableClub 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 ComputableSet 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 ComputableStable 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 ComputableSyllogism (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 ComputableEquivalent 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 ComputableEquivalent 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 ComputableVenn 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 ComputableLaw 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 ComputablePeano 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 ComputableRule 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 ComputableZermelo–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 ComputableConstructive 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 (orType 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 ComputableEpsilon-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 ComputableAxiom 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 ComputableMathematical 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 ComputableContraposition (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 ComputablePhilosophy 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 otherPrincipia 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 theFoundations 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 ComputableNew 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 ComputableSatisfiability 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 ComputableBoolean 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 ComputableLogicism (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 assertionsPropositional 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 decimalModel 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 ComputableEquality (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 ComputableUltrafilter 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 ComputableNatural 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 ComputableChurch 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 ComputableCardinality (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 ComputableConjunction/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 ComputableFirst-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 ComputablePropositional 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 ComputableVon 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 ofTuring'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 ComputableCantor'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 ComputableImplementation 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 ComputableList 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 slightlyList 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 ComputableList 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 dynamicistHilbert 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 ComputableGlossary 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