Forcing and satisfaction in Kripke models of intuitionistic arithmetic

Author:

Abiri Maryam1,Moniri Morteza1,Zaare Mostafa2

Affiliation:

1. Department of Mathematics, Shahid Beheshti University, G. C., Evin, Tehran, Iran

2. School of Mathematics and Computer Science, Damghan University, Damghan, Iran

Abstract

Abstract We define a class of first-order formulas $\mathsf{P}^{\ast }$ which exactly contains formulas $\varphi$ such that satisfaction of $\varphi$ in any classical structure attached to a node of a Kripke model of intuitionistic predicate logic deciding atomic formulas implies its forcing in that node. We also define a class of $\mathsf{E}$-formulas with the property that their forcing coincides with their classical satisfiability in Kripke models which decide atomic formulas. We also prove that any formula with this property is an $\mathsf{E}$-formula. Kripke models of intuitionistic arithmetical theories usually have this property. As a consequence, we prove a new conservativity result for Peano arithmetic over Heyting arithmetic.

Publisher

Oxford University Press (OUP)

Subject

Logic

Reference5 articles.

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Not all Kripke models of HA are locally PA;Advances in Mathematics;2022-03

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