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Heyting arithmetic

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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Axiomatization

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Unprovable statements

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Heyting arithmetic

Nodes110
Edges109
Triples93
Avg. degree1.98
Density0.018182
Components1

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Heyting arithmetic

Top relations

related to Unprovable classical principles · 17
Heyting arithmetic → Already, But, De Morgan's, Gödel's, HA, Heyting, However, In, LNP, Now, PA, PEM, Since, So, The, WLPO, WPEM
related to Extensions · 15
Heyting arithmetic → Ackermann, Beyond, Brouwerian, But, Church’s, Early, HA, Heyting, However, Kőnig's, Many, Markov's, Pi, That, The
related to Consistency and Soundness · 14
Heyting arithmetic → Con, Conversely, Gödel's, HA, Heyting, However, If, Kurt Gödel, NEP, PA, Peano, Sigma, So, That
related to Axiomatization · 12
Heyting arithmetic → HA, Heyting, In, IQC, Note, PA, Peano, PEM, S0, The, This, With
related to Excluded middle · 11
Heyting arithmetic → Any, As, By, HA, Heyting, Indeed, One, PEM, Sn, So, Stronger
related to Double negations · 6
Heyting arithmetic → Constructively, For, Heyting, Indeed, So, With
related to External links · 6
Heyting arithmetic → Fragments, Intuitionistic Number Theory, Joan Moschovakis, Philosophy, Stanford Encyclopedia, Wolfgang Burr
related to Unprovable statements · 6
Heyting arithmetic → DP, For, Given, Heyting, If, Independence
related to Related concepts · 2
Heyting arithmetic → Boolean, Heyting

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Important terminology

displaystyle theory mathrm mathsf neg ha also arithmetic heyting pa one predicate constructive equivalent principle independent exists existence classical induction

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
H Ainstance ofin rather conservative constructive frameworks0.80text
C Z Finstance ofthis and its numerical generalization are also exhibited by constructive second-order arithmetic and common set theories0.80text
P Ainstance ofTheories0.80text
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 functioninstance ofIt implies negations0.80text
Heyting arithmeticrelated to AxiomatizationHeyting0.60section
Heyting arithmeticrelated to AxiomatizationPeano0.60section
Heyting arithmeticrelated to AxiomatizationPA0.60section
Heyting arithmeticrelated to AxiomatizationIQC0.60section
Heyting arithmeticrelated to AxiomatizationIn0.60section
Heyting arithmeticrelated to AxiomatizationPEM0.60section
Heyting arithmeticrelated to AxiomatizationNote0.60section
Heyting arithmeticrelated to AxiomatizationHA0.60section

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