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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, i.e. 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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