Journal of Symbolic Logic

Bimodal Logics for Extensions of Arithmetical Theories

Lev D. Beklemishev

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We characterize the bimodal provability logics for certain natural (classes of) pairs of recursively enumerable theories, mostly related to fragments of arithmetic. For example, we shall give axiomatizations, decision procedures, and introduce natural Kripke semantics for the provability logics of $(I\Delta_0 + EXP, PRA); (PRA, I\Sigma_1); (I\Sigma_m, I\Sigma_n)$ for $1 \leq m < n; (PA, ACA_0); (ZFC, ZFC + CH); (ZFC, ZFC + \neg CH)$ etc. For the case of finitely axiomatized extensions of theories these results are extended to modal logics with propositional constants.

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J. Symbolic Logic, Volume 61, Issue 1 (1996), 91-124.

First available in Project Euclid: 6 July 2007

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Beklemishev, Lev D. Bimodal Logics for Extensions of Arithmetical Theories. J. Symbolic Logic 61 (1996), no. 1, 91--124.

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