About: Church's thesis (constructive mathematics)

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In constructive mathematics, Church's thesis (CT) is an axiom stating 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.

Attributes	Values
rdfs:label	Church's thesis (constructive mathematics) (en)
rdfs:comment	In constructive mathematics, Church's thesis (CT) is an axiom stating 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. (en)
sameAs	Church's thesis (constructive mathematics)
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:Not_a_typo dbt:Reflist
Subject	Constructivism (mathematics)
gold:hypernym	Axiom
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Church's_thesis_(constructive_mathematics)?oldid=944909859&ns=0
Wikipage page ID	15756448 (xsd:integer)
page length (characters) of wiki page	6145 (xsd:nonNegativeInteger)
Wikipage revision ID	944909859 (xsd:integer)
Link from a Wikipage to another Wikipage	Logical disjunction Disjunction and existence properties Andrey Markov Jr. Tautology (logic) Constructivism (mathematics) Quantifier (logic) Witness (mathematics) Church–Turing thesis Classical logic Computable function Constructivism (philosophy of mathematics) Effective method Heyting arithmetic Elliott Mendelson Equiconsistency Gödel numbering Peano axioms Kleene's T predicate The Journal of Philosophy Law of excluded middle Markov's principle Realizability
has abstract	In constructive mathematics, Church's thesis (CT) is an axiom stating 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. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Church's_thesis_(constructive_mathematics)
is Wikipage redirect of	Extended Church's thesis
is Link from a Wikipage to another Wikipage of	Disjunction and existence properties Church's (disambiguation) Church–Turing thesis Constructive set theory Indecomposability (intuitionistic logic) Markov's principle Extended Church's thesis
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Church's_thesis_(constructive_mathematics)

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