Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Heyting_arithmetic> ?p ?o. }
Showing items 1 to 19 of
19
with 100 items per page.
- Heyting_arithmetic abstract "In mathematical logic, Heyting arithmetic (sometimes abbreviated HA) is an axiomatization of arithmetic in accordance with the philosophy of intuitionism (Troelstra 1973:18). It is named after Arend Heyting, who first proposed it.Heyting arithmetic adopts the axioms of Peano arithmetic (PA), but uses intuitionistic logic as its rules of inference. In particular, the law of the excluded middle does not hold in general, though the induction axiom can be used to prove many specific cases. For instance, one can prove that ∀ x, y ∈ N : x = y ∨ x ≠ y is a theorem (any two natural numbers are either equal to each other, or not equal to each other). In fact, since "=" is the only predicate symbol in Heyting arithmetic, it then follows that, for any quantifier-free formula p, ∀ x, y, z, … ∈ N : p ∨ ¬p is a theorem (where x, y, z… are the free variables in p).Kurt Gödel studied the relationship between Heyting arithmetic and Peano arithmetic. He used the Gödel–Gentzen negative translation to prove in 1933 that if HA is consistent, then PA is also consistent.Heyting arithmetic should not be confused with Heyting algebras, which are the intuitionistic analogue of Boolean algebras.".
- Heyting_arithmetic wikiPageExternalLink IntNumTheHeyAri.
- Heyting_arithmetic wikiPageExternalLink www.math.uni-muenster.de%2Fu%2Fburr%2FHA.ps&ei=1xokUNzGBtOzhAeOhoDACg&usg=AFQjCNHBfKqVZwzEo2FgnF9Eia_Cmo4OZg.
- Heyting_arithmetic wikiPageID "2545815".
- Heyting_arithmetic wikiPageRevisionID "591221528".
- Heyting_arithmetic hasPhotoCollection Heyting_arithmetic.
- Heyting_arithmetic subject Category:Constructivism_(mathematics).
- Heyting_arithmetic subject Category:Intuitionism.
- Heyting_arithmetic comment "In mathematical logic, Heyting arithmetic (sometimes abbreviated HA) is an axiomatization of arithmetic in accordance with the philosophy of intuitionism (Troelstra 1973:18). It is named after Arend Heyting, who first proposed it.Heyting arithmetic adopts the axioms of Peano arithmetic (PA), but uses intuitionistic logic as its rules of inference. In particular, the law of the excluded middle does not hold in general, though the induction axiom can be used to prove many specific cases.".
- Heyting_arithmetic label "Aritmética de Heyting".
- Heyting_arithmetic label "Aritmética de Heyting".
- Heyting_arithmetic label "Heyting arithmetic".
- Heyting_arithmetic sameAs Aritmética_de_Heyting.
- Heyting_arithmetic sameAs Aritmética_de_Heyting.
- Heyting_arithmetic sameAs m.07m609.
- Heyting_arithmetic sameAs Q5548813.
- Heyting_arithmetic sameAs Q5548813.
- Heyting_arithmetic wasDerivedFrom Heyting_arithmetic?oldid=591221528.
- Heyting_arithmetic isPrimaryTopicOf Heyting_arithmetic.