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In computability theory, a set of natural numbers is computable (or decidable or recursive) if there is an algorithm that computes the membership of everyJoel David Hamkins (1,791 words) [view diff] no match in snippet view article find links to article
theory (particularly the idea of the set-theoretic multiverse), in computability theory, and in group theory. After earning a Bachelor of Science inList of statements independent of ZFC (2,182 words) [view diff] no match in snippet view article find links to article
CH cannot be disproven in ZFC; Paul Cohen later invented the method of forcing to exhibit a model of ZFC in which CH fails, showing that CH cannot beDecision 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 aMathematical 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 mathematicalList of mathematical logic topics (1,012 words) [view diff] no match in snippet view article find links to article
syllogistic logic, see the list of topics in logic. See also the list of computability and complexity topics for more theory of algorithms. Peano axioms GiuseppeLow basis theorem (570 words) [view diff] no match in snippet view article find links to article
The low basis theorem is one of several basis theorems in computability theory, each of which show that, given an infinite subtree of the binary treeUndecidable 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 constructComputable 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 computesComputability 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 originatedComputably 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 decidableFormal language (3,163 words) [view diff] no match in snippet view article find links to article
expensive). Therefore, formal language theory is a major application area of computability theory and complexity theory. Formal languages may be classified inDecidability (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 decidabilityTimeline of mathematical logic (948 words) [view diff] no match in snippet view article find links to article
presents "Turing's Thesis", asserting the identity of computability in general with computability by Turing machines, as an equivalent form of Church'sEnumeration (1,633 words) [view diff] no match in snippet view article find links to article
onto S need not imply the existence of an injection from S into I. In computability theory one often considers countable enumerations with the added requirementChurch–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'sHalting 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, whetherList of formal systems (284 words) [view diff] no match in snippet view article find links to article
Formal system – Mathematical model for deduction or proof systems Computability:Formal models Model of computation – Mathematical model describing howRobert I. Soare (171 words) [view diff] no match in snippet view article find links to article
has done other work in mathematical logic, primarily in the area of computability theory. His doctoral students at the University of Chicago have includedSlicing the Truth (768 words) [view diff] no match in snippet view article find links to article
also review some of the tools needed in this study, including computability theory, forcing, and the low basis theorem. Chapter six, "the real heart ofEntscheidungsproblem (2,642 words) [view diff] no match in snippet view article find links to article
history leading to, and a discussion of, his proof. Soare, Robert I., "Computability and recursion", Bull. Symbolic Logic 2 (1996), no. 3, 284–321. ToulminTuring machine (9,386 words) [view diff] no match in snippet view article find links to article
of Turing machines has yielded many insights into computer science, computability theory, and complexity theory. In his 1948 essay, "Intelligent Machinery"Primitive recursive function (7,342 words) [view diff] no match in snippet view article find links to article
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are allGeneric filter (341 words) [view diff] no match in snippet view article find links to article
examplesPages displaying short descriptions of redirect targets in computability Rasiowa–Sikorski lemma – Mathematical lemma K. Ciesielski (1997). SetLindström's theorem (386 words) [view diff] no match in snippet view article find links to article
first course in logic: an introduction to model theory, proof theory, computability, and complexity, Oxford University Press, 2004, ISBN 0-19-852981-3,Course-of-values recursion (1,299 words) [view diff] no match in snippet view article find links to article
In computability theory, course-of-values recursion is a technique for defining number-theoretic functions by recursion. In a definition of a functionElementary diagram (182 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableStrength (mathematical logic) (83 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableNon-standard model (105 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableReverse mathematics (4,782 words) [view diff] no match in snippet view article find links to article
establish a close link between the complexity of a formula and the (non)computability of the set it defines. Another effect of using second-order arithmeticAbstract logic (143 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMartin's axiom (806 words) [view diff] no match in snippet view article find links to article
Rasiowa–Sikorski lemma. It is a principle that is used to control certain forcing arguments. For a cardinal number κ, define the following statement: MA(κ)Elementary function arithmetic (875 words) [view diff] no match in snippet view article find links to article
kind of mathematical function Grzegorczyk hierarchy – Functions in computability theory Reverse mathematics – Branch of mathematical logic Ordinal analysis –Truth predicate (230 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableDiagram (mathematical logic) (314 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableKolmogorov complexity (7,896 words) [view diff] no match in snippet view article find links to article
14words". It is also possible to show the non-computability of K by reduction from the non-computability of the halting problem H, since K and H are Turing-equivalentHereditary set (279 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableModel complete theory (557 words) [view diff] no match in snippet view article find links to article
Wheeler, William H. (1975). "Model-completions and model-companions". Forcing, Arithmetic, Division Rings. Lecture Notes in Mathematics. Vol. 454. SpringerLambda calculus (12,168 words) [view diff] no match in snippet view article find links to article
computable by any model of computation that is Turing complete. In fact computability can itself be defined via the lambda calculus: a function F: N → N ofEquiconsistency (732 words) [view diff] no match in snippet view article find links to article
is ZFC or an extension of it, the notion is meaningful. The method of forcing allows one to show that the theories ZFC, ZFC+CH and ZFC+¬CH are all equiconsistentAxiom of global choice (458 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableJames Earl Baumgartner (471 words) [view diff] no match in snippet view article find links to article
and Jaakko Hintikka, editors, Logic, Foundations of Mathematics and Computability Theory, pages 87–106. Reidel, 1977 Baumgartner, James E.; Galvin, FredPropositional variable (442 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSoundness (1,098 words) [view diff] no match in snippet view article find links to article
Macmillan Publishing Co., ISBN 0-02-324880-7 Boolos, Burgess, Jeffrey. Computability and Logic, 4th Ed, Cambridge, 2002. Wiktionary has definitions relatedAxiom schema (470 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFormation rule (442 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableInfinite set (917 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableQuantifier rank (516 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableGeneral set theory (1,235 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLemma (mathematics) (399 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableExtensionality (618 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableUncountable set (884 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableElement (mathematics) (1,031 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableClassical logic (841 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFallibilism (2,886 words) [view diff] no match in snippet view article find links to article
hypothesis. The second type of undecidability is used in relation to computability theory (or recursion theory) and applies not solely to statements butPredicate variable (560 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTransfinite induction (1,142 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableReduct (264 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableRasiowa–Sikorski lemma (424 words) [view diff] no match in snippet view article find links to article
one of the most fundamental facts used in the technique of forcing. In the area of forcing, a subset E of a poset (P, ≤) is called dense in P if for anyIndependence (mathematical logic) (519 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLogical constant (289 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAtomic formula (523 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTarski–Grothendieck set theory (1,135 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAxiom of adjunction (480 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTransitive set (1,222 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSymbol (formal) (494 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSentence (mathematical logic) (458 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTruth value (862 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableUrelement (995 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableT-schema (584 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMap (mathematics) (708 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableRobinson arithmetic (1,839 words) [view diff] no match in snippet view article find links to article
JSTOR 2272251. Boolos, George; Burgess, John P.; Jeffrey, Richard (2002). Computability and Logic (4th ed.). Cambridge University Press. ISBN 0-521-00758-5Uninterpreted function (410 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCantor's paradox (734 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableWell-formed formula (2,164 words) [view diff] no match in snippet view article find links to article
(1): 29–41 Boolos, George; Burgess, John; Jeffrey, Richard (2002), Computability and Logic (4th ed.), Cambridge University Press, ISBN 978-0-521-00758-0Universal set (1,327 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputablePredicate (logic) (421 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFree logic (973 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFormal proof (579 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableContinuum hypothesis (4,060 words) [view diff] no match in snippet view article find links to article
independence proof. To prove his result, Cohen developed the method of forcing, which has become a standard tool in set theory. Essentially, this methodGround expression (656 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCompactness theorem (1,931 words) [view diff] no match in snippet view article find links to article
Hodges (1993). Boolos, George; Jeffrey, Richard; Burgess, John (2004). Computability and Logic (fourth ed.). Cambridge University Press. Chang, C.C.; KeislerFoundations of mathematics (6,910 words) [view diff] no match in snippet view article find links to article
mathematical logic that includes set theory, model theory, proof theory, computability and computational complexity theory, and more recently, parts of computerGödel numbering (1,536 words) [view diff] no match in snippet view article find links to article
about the consistency and completeness properties of formal systems. In computability theory, the term "Gödel numbering" is used in settings more generalAbstract model theory (169 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLogical equivalence (751 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableNon-standard model of arithmetic (1,292 words) [view diff] no match in snippet view article find links to article
countable dense linear order. Boolos, George, and Jeffrey, Richard 1974. Computability and Logic, Cambridge University Press. ISBN 0-521-38923-2. Skolem, ThoralfUniqueness quantification (848 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMonadic predicate calculus (698 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableIntersection (set theory) (1,734 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSpectrum of a sentence (1,365 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSatisfiability (1,500 words) [view diff] no match in snippet view article find links to article
(MIT Press). Boolos, George; Burgess, John; Jeffrey, Richard (2007). Computability and Logic (5th ed.). Cambridge University Press. Daniel Kroening; OferSemantic theory of truth (1,050 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSubstructure (mathematics) (754 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableClass (set theory) (1,279 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSelf-verifying theories (419 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAxiom of constructibility (1,064 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableKripke–Platek set theory (1,586 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableComplete theory (396 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSpectrum of a theory (1,132 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableGödel's incompleteness theorems (12,165 words) [view diff] no match in snippet view article find links to article
second sense, which will not be discussed here, is used in relation to computability theory and applies not to statements but to decision problems, whichSemantics of logic (707 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSaturated model (1,096 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTarski's undefinability theorem (2,271 words) [view diff] no match in snippet view article find links to article
Logic. North-Holland. Boolos, G.; Burgess, J.; Jeffrey, R. (2002). Computability and Logic (4th ed.). Cambridge University Press. Lucas, J. R. (1961)Axiom of dependent choice (950 words) [view diff] no match in snippet view article find links to article
converse is proved in Boolos, George S.; Jeffrey, Richard C. (1989). Computability and Logic (3rd ed.). Cambridge University Press. pp. 155–156. ISBN 0-521-38026-XAczel's anti-foundation axiom (273 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableHigher-order logic (1,066 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableApartness relation (646 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableArity (1,464 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableUnion (set theory) (1,967 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLarge cardinal (1,333 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableDomain of a function (962 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableValidity (logic) (1,110 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableComplement (set theory) (1,515 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSet theory (6,586 words) [view diff] no match in snippet view article find links to article
of forcing while searching for a model of ZFC in which the continuum hypothesis fails, or a model of ZF in which the axiom of choice fails. Forcing adjoinsC-minimal theory (421 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMathematical structure (650 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSignature (logic) (1,339 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableExtension by new constant and function names (425 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAlphabet (formal languages) (843 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableEmpty set (2,229 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMostowski collapse lemma (591 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSubset (1,734 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMonadic second-order logic (1,308 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableOpen formula (394 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableRobinson's joint consistency theorem (321 words) [view diff] no match in snippet view article find links to article
test Boolos, George S.; Burgess, John P.; Jeffrey, Richard C. (2002). Computability and Logic. Cambridge University Press. p. 264. ISBN 0-521-00758-5. RobinsonCompleteness (logic) (771 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableNon-logical symbol (783 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAleph number (2,453 words) [view diff] no match in snippet view article find links to article
the CH itself is not a theorem of ZFC – by the (then-novel) method of forcing. Aleph-omega is ℵ ω = sup { ℵ n | n ∈ ω } = sup { ℵ n | n ∈ { 0 , 1 , 2Setoid (532 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLogical equality (614 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCodomain (1,051 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableDiagonal intersection (386 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableInhabited set (1,358 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAtomic model (mathematical logic) (344 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableRange of a function (830 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSyntax (logic) (1,052 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableŁoś–Vaught test (235 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableElementary equivalence (956 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputablePower set (2,479 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableList of mathematical proofs (593 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableBeth definability (315 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableHistory of logic (13,255 words) [view diff] no match in snippet view article find links to article
research: model theory, proof theory, computability theory, and set theory. In set theory, the method of forcing revolutionized the field by providingExtension by definition (1,506 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableArgument of a function (440 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableBinary operation (1,546 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMetavariable (329 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableExistential quantification (1,535 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFinite-valued logic (1,322 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCategorical theory (1,157 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMetavariable (329 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputablePrime model (508 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableZermelo–Fraenkel set theory (6,282 words) [view diff] no match in snippet view article find links to article
Since forcing preserves choice, we cannot directly produce a model contradicting choice from a model satisfying choice. However, we can use forcing to createInfinite-valued logic (1,479 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableInstitutional model theory (358 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableElementary proof (623 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFinite set (2,594 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputablePrimitive recursive arithmetic (1,378 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableNon-well-founded set theory (1,479 words) [view diff] no match in snippet view article find links to article
Mathématique de Belgique, 20: 3–15, Zbl 0179.01602 Boffa, M. (1972), "Forcing et négation de l'axiome de Fondement", Acad. Roy. Belgique, Mém. Cl. SciStratification (mathematics) (820 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFunctional predicate (1,254 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable 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 aGrothendieck universe (1,342 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableVon Neumann cardinal assignment (651 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFodor's lemma (475 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAutomated theorem proving (2,933 words) [view diff] no match in snippet view article find links to article
on the one hand gave two independent but equivalent definitions of computability, and on the other gave concrete examples of undecidable questions. InProof without words (931 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableParadoxes of set theory (2,657 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableConservative extension (888 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMetalanguage (1,418 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableWeakly o-minimal structure (508 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLogical conjunction (1,465 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAxiomatic system (1,765 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLogical truth (1,094 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputablePeano axioms (6,478 words) [view diff] no match in snippet view article find links to article
Kaye 1991, Section 11.3. Kaye 1991, pp. 70ff.. Davis, Martin (1974). Computability. Notes by Barry Jacobs. Courant Institute of Mathematical Sciences,Richard's paradox (1,800 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAtomic sentence (1,196 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFinitary relation (1,905 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableVon Neumann universe (2,818 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTheorem (4,409 words) [view diff] no match in snippet view article find links to article
1994, p. 104. Boolos, George; Burgess, John; Jeffrey, Richard (2007). Computability and Logic (5th ed.). Cambridge University Press. Enderton, Herbert (2001)Richardson's theorem (701 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTarski's theorem about choice (583 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTheory (mathematical logic) (1,695 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSurjective function (1,941 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAlgebra of sets (1,865 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFormal system (1,544 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLogical consequence (1,910 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableInjective function (2,589 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableBijection (2,508 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableOrdered pair (3,697 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableType (model theory) (2,253 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableHilbert's second problem (1,500 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableRegular cardinal (1,437 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableBack-and-forth method (688 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAmalgamation property (817 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableInterpretation (model theory) (824 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableProof by exhaustion (940 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableProof by exhaustion (940 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCardinal number (3,834 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableO-minimal theory (1,294 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableHilbert's axioms (2,313 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSchröder–Bernstein theorem (2,374 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableModel-theoretic grammar (526 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableContradiction (2,673 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableIdentity type (406 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableNegation (2,236 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableExtender (set theory) (701 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCountable set (4,381 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMathematical object (2,769 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableExpression (mathematics) (5,319 words) [view diff] no match in snippet view article
Norton & Company. ISBN 978-0-393-04785-1. Davis, Martin (1982-01-01). Computability & Unsolvability. Courier Corporation. ISBN 978-0-486-61471-7. TuringUniversal quantification (2,503 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCartesian product (3,944 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTransfer principle (2,686 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMorse–Kelley set theory (3,186 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLogical disjunction (1,937 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSupertask (2,391 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAxiom (4,918 words) [view diff] no match in snippet view article find links to article
Zermelo–Fraenkel axioms for set theory. Furthermore, using techniques of forcing (Cohen) one can show that the continuum hypothesis (Cantor) is independentWell-founded relation (1,378 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableGödel's completeness theorem (2,330 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableUniverse (mathematics) (2,649 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCantor's diagonal argument (2,808 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSubstitution (logic) (2,938 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCantor's theorem (3,735 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMaterial conditional (2,229 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAlgebraic logic (2,220 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMathematical and theoretical biology (4,322 words) [view diff] no match in snippet view article find links to article
1513–1577. Lin HC (2004). "Computer Simulations and the Question of Computability of Biological Systems" (PDF). Computer Models and Automata Theory inComputer-assisted proof (2,059 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAda Lovelace (9,797 words) [view diff] no match in snippet view article find links to article
Computability". Ada Lovelace Day. FindingAda.com. 31 January 2016. Retrieved 11 January 2016. "The Ada Lovelace Bicentenary Lectures on Computability"Joint embedding property (320 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableNaive set theory (4,782 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableEquivalence relation (4,473 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableBoolean function (2,887 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSet (mathematics) (7,143 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableRecursion (3,669 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableStrongly minimal theory (405 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSuccessor cardinal (564 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableList of first-order theories (5,269 words) [view diff] no match in snippet view article find links to article
hypothesis), Martin's maximum ◊ and ♣ Axiom of constructibility (V=L) Proper forcing axiom Analytic determinacy, projective determinacy, Axiom of determinacyNP (complexity) (2,784 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableUltraproduct (3,087 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSquare of opposition (3,161 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableInaccessible cardinal (2,405 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTerm (logic) (2,808 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableProof by contradiction (2,602 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableConsistency (2,931 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableRoss–Littlewood paradox (1,264 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableRussell's paradox (4,621 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableAxiom of choice (7,923 words) [view diff] no match in snippet view article find links to article
ZF itself is consistent. In 1963, Paul Cohen employed the technique of forcing, developed for this purpose, to show that, assuming ZF is consistent, theRussell's paradox (4,621 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFinite model theory (3,093 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLogical connective (3,164 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFunctional completeness (1,957 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFormal grammar (3,450 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLöwenheim–Skolem theorem (2,795 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableDecidability of first-order theories of the real numbers (503 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableKőnig's theorem (set theory) (1,232 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFraïssé limit (1,388 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableVariable (mathematics) (3,793 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTarski's axioms (3,825 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableGentzen's consistency proof (1,993 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableVenn diagram (3,242 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCardinal assignment (589 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableStructural induction (1,750 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTerm logic (3,903 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSkolem's paradox (3,331 words) [view diff] no match in snippet view article find links to article
the study of set theory. Paul Cohen's method for extending set theory, forcing, is often explained in terms of countable models, and was described byList of axiomatic systems in logic (3,906 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableThree-valued logic (3,292 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLogical biconditional (1,794 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableConstructible universe (6,103 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableConstructive set theory (35,229 words) [view diff] no match in snippet view article find links to article
standard axioms to classically equivalent ones. Apart from demands for computability and reservations regrading of impredicativity, technical question regardingLaw of noncontradiction (3,139 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableList of superseded scientific theories (3,004 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMathematical proof (4,229 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFeferman–Vaught theorem (1,233 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTruth table (3,307 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFixed-point logic (2,031 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableArgument (4,260 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableUnbounded nondeterminism (2,718 words) [view diff] no match in snippet view article find links to article
could theoretically solve the halting problem, a famous challenge in computability theory that asks whether a Turing machine will stop or continue foreverClub filter (754 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableQuantifier (logic) (4,501 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableKurt Gödel (5,947 words) [view diff] no match in snippet view article find links to article
Mathematical Society. During this year, Gödel also developed the ideas of computability and recursive functions to the point where he was able to present aSecond-order logic (4,502 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableInterpretation (logic) (4,478 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableProof of impossibility (3,915 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputablePhilosophy of mathematics (10,555 words) [view diff] no match in snippet view article find links to article
advocated by mathematical intuitionists and constructivists in the "computability" tradition—. The French mathematician Henri Poincaré was among the firstTruth-value semantics (632 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableProof by infinite descent (2,223 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableZorn's lemma (4,665 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSyllogism (5,135 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableInduction, bounding and least number principles (1,211 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableRule of inference (7,327 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableNew Foundations (8,162 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableDeterminacy (4,125 words) [view diff] no match in snippet view article find links to article
1142/9789812564894_0005. ISBN 978-981-02-4736-2. Soare, Robert I. (2016). Turing Computability: Theory and Applications. Springer. pp. 217ff. ISBN 978-3-6423-1932-7Structure (mathematical logic) (5,140 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableModel theory (9,064 words) [view diff] no match in snippet view article find links to article
Gödel's work on the constructible universe, which, along with the method of forcing developed by Paul Cohen can be shown to prove the (again philosophicallyLaw of excluded middle (5,601 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableCardinality (11,564 words) [view diff] no match in snippet view article find links to article
independent from ZFC. To prove his result, Cohen developed the method of forcing, which has become a standard tool in set theory. Essentially, this methodVon Neumann–Bernays–Gödel set theory (15,666 words) [view diff] no match in snippet view article find links to article
factors, including the extra work required to handle forcing in NBG, Cohen's 1966 presentation of forcing, which used ZF, and the proof that NBG is a conservativeUltrafilter on a set (7,379 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableStable theory (3,633 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputablePrincipia Mathematica (9,478 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableType theory (8,230 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableProof sketch for Gödel's first incompleteness theorem (2,988 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableMathematical induction (6,914 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTimeline of mathematics (7,870 words) [view diff] no match in snippet view article find links to article
λ-calculus and the Turing machine, formalizing the notion of computation and computability. 1938 – Tadeusz Banachiewicz introduces LU decomposition. 1940 – KurtEquivalent definitions of mathematical structures (3,272 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableTarski's high school algebra problem (1,991 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableBoolean algebra (9,571 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableContraposition (6,175 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputablePropositional formula (11,131 words) [view diff] no match in snippet view article find links to article
Library of Congress Catalog Card Number 67-12342. Useful especially for computability, plus good sources. Joel W. Robbin 1969, 1997, Mathematical Logic: AEquality (mathematics) (7,795 words) [view diff] no match in snippet view article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableSatisfiability modulo theories (4,371 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableEpsilon-induction (4,195 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableNoam Chomsky (18,675 words) [view diff] no match in snippet view article find links to article
December 9, 2015. Davis, Martin; Weyuker, Elaine J.; Sigal, Ron (1994). Computability, complexity, and languages: fundamentals of theoretical computer scienceNatural deduction (7,755 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableChurch encoding (8,556 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableFirst-order logic (12,955 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputablePropositional logic (11,449 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableLogicism (11,833 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableHistory of mathematics (17,048 words) [view diff] no match in snippet view article find links to article
areas of mathematics were developed to deal with this: Alan Turing's computability theory; complexity theory; Derrick Henry Lehmer's use of ENIAC to furtherTuring's proof (7,140 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableList of women in mathematics (23,412 words) [view diff] no match in snippet view article find links to article
1957), Portuguese and Swiss stochastic analyst Barbara Csima, Canadian computability theorist, president of Canadian Mathematical Society Marianna CsörnyeiCantor's first set theory article (7,563 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableConjunction/disjunction duality (1,337 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableList of set identities and relations (29,862 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable ComputableImplementation of mathematics in set theory (10,960 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable 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 behaviorHilbert system (3,534 words) [view diff] no match in snippet view article find links to article
Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable