Classical and Intuitionistic Models of Arithmetic

Notre Dame Journal of Formal Logic 37 (3):452-461 (1996)
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Abstract

Given a classical theory T, a Kripke model K for the language L of T is called T-normal or locally PA just in case the classical L-structure attached to each node of K is a classical model of T. Van Dalen, Mulder, Krabbe, and Visser showed that Kripke models of Heyting Arithmetic (HA) over finite frames are locally PA, and that Kripke models of HA over frames ordered like the natural numbers contain infinitely many PA-nodes. We show that Kripke models of the latter sort are in fact PA-normal. This result is extended to a somewhat larger class of frames.

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Kai Wehmeier
University of California, Irvine

References found in this work

Intuitionistic Validity in T-Normal Kripke Structures.Samuel R. Buss - 1993 - Annals of Pure and Applied Logic 59 (3):159-173.
On the Structure of Kripke Models of Heyting Arithmetic.Zoran Marković - 1993 - Mathematical Logic Quarterly 39 (1):531-538.
Finite Kripke Models of HA Are Locally PA.E. C. W. Krabbe - 1986 - Notre Dame Journal of Formal Logic 27:528-532.

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