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Propositional logics of closed and open substitutions over Heyting’s Arithmetic

By A. Visser


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

Topics: Wijsbegeerte
Year: 2005
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