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2006 Propositional Logics of Closed and Open Substitutions over Heyting's Arithmetic
Albert Visser
Notre Dame J. Formal Logic 47(3): 299-309 (2006). DOI: 10.1305/ndjfl/1163775437

Abstract

In this note we compare propositional logics for closed substitutions and propositional logics for open substitutions in constructive arithmetical theories. We provide a strong example where these logics diverge in an essential way. We prove that for Markov's Arithmetic, that is, Heyting's Arithmetic plus Markov's principle plus Extended Church's Thesis, the logic of closed and the logic of open substitutions are the same.

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Albert Visser. "Propositional Logics of Closed and Open Substitutions over Heyting's Arithmetic." Notre Dame J. Formal Logic 47 (3) 299 - 309, 2006. https://doi.org/10.1305/ndjfl/1163775437

Information

Published: 2006
First available in Project Euclid: 17 November 2006

zbMATH: 1113.03053
MathSciNet: MR2264699
Digital Object Identifier: 10.1305/ndjfl/1163775437

Subjects:
Primary: 03F50
Secondary: 03B20, 03F30

Rights: Copyright © 2006 University of Notre Dame

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Vol.47 • No. 3 • 2006
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