Embedding intuitionistic-type theory in negationless-type theory

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1986 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 39, pages 66-74 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Krivtsov, V. N.;

doi: 10.1007/bf01647635

Embedding intuitionistic-type theory in negationless-type theory

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Abstract

In ''A formal system of negationless arithmetic that is consistent with respect to Heyting arithmetic'' [Mat. Zametki 36, No.4, 583-592 (1984; Zbl 0576.03037)] the author shows that Heyting arithmetic is a conservative extension of \(HA^ N\)- a system of negationless arithmetic, under certain interpretation. Here he extends this result to the case of intuitionistic type theory HATT and a system of negationless type theory HATTN.

Related Organizations

Lomonosov Moscow State University
Russian Federation

Keywords

Heyting arithmetic, negationless type theory, intuitionistic type theory, Intuitionistic mathematics, Relative consistency and interpretations

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