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In mathematical logic, Heyting arithmetic H A {\displaystyle {\mathsf {HA}}} is an axiomatization of arithmetic in accordance with the philosophy of intuitionism. It is named after Arend Heyting, who first proposed it.
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displaystyle theory mathrm mathsf neg ha also arithmetic heyting pa one predicate constructive equivalent principle independent exists existence classical induction
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| H A | instance of | in rather conservative constructive frameworks | 0.80 | text |
| C Z F | instance of | this and its numerical generalization are also exhibited by constructive second-order arithmetic and common set theories | 0.80 | text |
| P A | instance of | Theories | 0.80 | text |
| the ones just described.Consider the principle in the form stating that all predicates that are decidable in the logic sense above are also decidable by a total computable function | instance of | It implies negations | 0.80 | text |
| Heyting arithmetic | related to Axiomatization | Heyting | 0.60 | section |
| Heyting arithmetic | related to Axiomatization | Peano | 0.60 | section |
| Heyting arithmetic | related to Axiomatization | PA | 0.60 | section |
| Heyting arithmetic | related to Axiomatization | IQC | 0.60 | section |
| Heyting arithmetic | related to Axiomatization | In | 0.60 | section |
| Heyting arithmetic | related to Axiomatization | PEM | 0.60 | section |
| Heyting arithmetic | related to Axiomatization | Note | 0.60 | section |
| Heyting arithmetic | related to Axiomatization | HA | 0.60 | section |
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