Classical and intuitionistic models of arithmetic
type: Item
instance of: scholarly article
title: Classical and intuitionistic models of arithmetic
zbMATH Open document ID: 0871.03027
published in: Notre Dame Journal of Formal Logic
publication date: 1997-09-03T00:00:00Z
review text: A Kripke model of a theory \(T\), in a language \(L\), is a structure \({\mathbb{K}}=(K,\leq, (A_\alpha)_{\alpha\in K})\), where \((K,\leq)\) is a partial order, called the frame of \(\mathbb{K}\), and the structures \(A_\alpha\), for \(\alpha\in K\), are classical \(L\)-structures satisfying certain monotonicity conditions with respect to \(K\). \({\mathbb{K}}\) is locally \(T\) if all structures \(A_\alpha\) are classical models of \(T\). \textit{D. van Dalen, H. Mulder, E. C. Krabbe} and \textit{A. Visser} proved [Notre Dame J. Formal Logic 27, 528-532 (1986; Zbl 0632.03048)] that Kripke models of Heyting Arithmetic (HA) over finite frames are locally PA. Using the technique of pruning of van Dalen et al. [loc. cit.], the author shows that Kripke models of HA over the frame \((\omega,\leq)\) are locally PA. This result is then extended to some other types of infinite frames. The paper also presents other results concerning the conjecture: all Kripke models of HA are locally PA.
reviewed by: Roman Kossak
Mathematics Subject Classification ID: 03C62
zbMATH DE Number: 1011145
zbMATH Keywords: Heyting arithmetic
zbMATH Keywords: Kripke models
zbMATH Keywords: pruning
zbMATH Keywords: frame
zbMATH Keywords: locally PA
author: Kai Frederick Wehmeier
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1039886521
OpenAlex ID: W2088003715
DOI: 10.1305/NDJFL/1039886521
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description: scientific article; zbMATH DE number 1011145