Authors: | Marković, Zoran | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | On the structure of kripke models of heyting arithmetic | Journal: | Mathematical Logic Quarterly | Volume: | 39 | Issue: | 1 | First page: | 531 | Last page: | 538 | Issue Date: | 1-Jan-1993 | ISSN: | 0942-5616 | DOI: | 10.1002/malq.19930390154 | 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 IΔ1 (PA‐ with induction for provably Δ1 formulas) and that the relation between these classical structures must be that of a Δ1‐elementary submodel. MSC: 03F30, 03F55. |
Keywords: | Heyting arithmetic | Kripke model | Peano arithmetic |
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