Propositional Logics of Closed and Open Substitutions over Heyting's Arithmetic
Albert Visser
Source: Notre Dame J. Formal Logic Volume 47, Number 3
(2006), 299-309.
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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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1163775437
Digital Object Identifier: doi:10.1305/ndjfl/1163775437
Mathematical Reviews number (MathSciNet): MR2264699
Zentralblatt MATH identifier: 1113.03053
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