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On the structure of kripke models of heyting arithmetic

✍ Scribed by Zoran Marković

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
456 KB
Volume
39
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

Since in Heyting Arithmetic (HA) all atomic formulas are decidable, a Kripke model for HA may be regarded classically as a collection of classical structures for the language of arithmetic, partially ordered by the submodel relation. The obvious question is then: are these classical structures models of Peano Arithmetic (PA)? And dually: if a collection of models of PA, partially ordered by the submodel relation, is regarded as a Kripke model, is it a model of HA? Some partial answers to these questions were obtained in [6], [3], [1] and [2]. Here we present some results in the same direction, announced in [7]. In particular, it is proved that the classical structures at the nodes of a Kripke model of HA must be models of IΔ~1~ (PA^‐^ with induction for provably Δ~1~ formulas) and that the relation between these classical structures must be that of a Δ~1~‐elementary submodel. MSC: 03F30, 03F55.

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