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Summer 1996 Classical and Intuitionistic Models of Arithmetic
Kai F. Wehmeier
Notre Dame J. Formal Logic 37(3): 452-461 (Summer 1996). DOI: 10.1305/ndjfl/1039886521

Abstract

Given a classical theory T, a Kripke structure ${\bf K} = (K, \leq, (A_{\alpha})_{\alpha \in K})$ is called T-normal (or locally T) if for each $ \alpha \in K $, $ A_{\alpha} $ is a classical model of T. It has been known for some time now, thanks to van Dalen, Mulder, Krabbe, and Visser, that Kripke models of HA over finite frames $ (K, \leq) $ are locally ${\bf PA}$. They also proved that models of ${\bf HA}$ over the frame $ (\omega, \leq) $ contain infinitely many Peano nodes. We will show that such models are in fact ${\bf PA}$-normal, that is, they consist entirely of Peano nodes. These results are then applied to a somewhat larger class of frames. We close with some general considerations on properties of non-Peano nodes in arbitrary models of ${\bf HA}$.

Citation

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Kai F. Wehmeier. "Classical and Intuitionistic Models of Arithmetic." Notre Dame J. Formal Logic 37 (3) 452 - 461, Summer 1996. https://doi.org/10.1305/ndjfl/1039886521

Information

Published: Summer 1996
First available in Project Euclid: 14 December 2002

zbMATH: 0871.03027
MathSciNet: MR1434430
Digital Object Identifier: 10.1305/ndjfl/1039886521

Subjects:
Primary: 03F50
Secondary: 03C62, 03F55

Rights: Copyright © 1996 University of Notre Dame

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Vol.37 • No. 3 • Summer 1996
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