Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 47, Number 3 (2006), 299-309.
Propositional Logics of Closed and Open Substitutions over Heyting's Arithmetic
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.
Notre Dame J. Formal Logic, Volume 47, Number 3 (2006), 299-309.
First available in Project Euclid: 17 November 2006
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Visser, Albert. Propositional Logics of Closed and Open Substitutions over Heyting's Arithmetic. Notre Dame J. Formal Logic 47 (2006), no. 3, 299--309. doi:10.1305/ndjfl/1163775437. https://projecteuclid.org/euclid.ndjfl/1163775437