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- Churchs_thesis_(constructive_mathematics) abstract "In constructive mathematics, Church's thesis (CT) is an axiom which states that all total functions are computable. The axiom takes its name from the Church–Turing thesis, which states that every effectively calculable function is a computable function, but the constructivist version is much stronger, claiming that every function is computable.The axiom CT is incompatible with classical logic in sufficiently strong systems. For example, Heyting arithmetic (HA) with CT as an addition axiom is able to disprove some instances of the law of the excluded middle. However, Heyting arithmetic is equiconsistent with Peano arithmetic (PA) as well as with Heyting arithmetic plus Church's thesis. That is, adding either the law of the excluded middle or Church's thesis does not make Heyting arithmetic inconsistent, but adding both does.".
- Churchs_thesis_(constructive_mathematics) wikiPageID "15756448".
- Churchs_thesis_(constructive_mathematics) wikiPageLength "5912".
- Churchs_thesis_(constructive_mathematics) wikiPageOutDegree "20".
- Churchs_thesis_(constructive_mathematics) wikiPageRevisionID "656064576".
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Andrey_Markov,_Jr..
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Category:Constructivism_(mathematics).
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Church–Turing_thesis.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Classical_logic.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Computable_function.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Constructivism_(mathematics).
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Disjunction_and_existence_properties.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Effective_method.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Equiconsistency.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Gödel_numbering.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Heyting_arithmetic.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Kleenes_T_predicate.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Law_of_excluded_middle.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Logical_disjunction.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Markovs_principle.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Peano_axioms.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Quantifier_(logic).
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Realizability.
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLink Tautology_(logic).
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLinkText "Church's rule".
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLinkText "Church's thesis (constructive mathematics)".
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLinkText "Church's thesis in constructive mathematics".
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLinkText "Church's thesis".
- Churchs_thesis_(constructive_mathematics) wikiPageWikiLinkText "Extended Church's thesis".
- Churchs_thesis_(constructive_mathematics) wikiPageUsesTemplate Template:Not_a_typo.
- Churchs_thesis_(constructive_mathematics) subject Category:Constructivism_(mathematics).
- Churchs_thesis_(constructive_mathematics) hypernym Axiom.
- Churchs_thesis_(constructive_mathematics) type Theory.
- Churchs_thesis_(constructive_mathematics) comment "In constructive mathematics, Church's thesis (CT) is an axiom which states that all total functions are computable. The axiom takes its name from the Church–Turing thesis, which states that every effectively calculable function is a computable function, but the constructivist version is much stronger, claiming that every function is computable.The axiom CT is incompatible with classical logic in sufficiently strong systems.".
- Churchs_thesis_(constructive_mathematics) label "Church's thesis (constructive mathematics)".
- Churchs_thesis_(constructive_mathematics) sameAs Q5116527.
- Churchs_thesis_(constructive_mathematics) sameAs m.03nsgc6.
- Churchs_thesis_(constructive_mathematics) sameAs Q5116527.
- Churchs_thesis_(constructive_mathematics) wasDerivedFrom Churchs_thesis_(constructive_mathematics)?oldid=656064576.
- Churchs_thesis_(constructive_mathematics) isPrimaryTopicOf Churchs_thesis_(constructive_mathematics).