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Bimodal logics for extensions of arithmetical theories

Published online by Cambridge University Press:  12 March 2014

Lev D. Beklemishev
Lev D. Beklemishev*
Affiliation:
Steklov Mathematical Institute, Vavilov Str. 42, Moscow 117966, Russia, E-mail: lev@bekl.mian.su
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Abstract

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 (IΔ0 + EXP, PRA); (PRA, IΣn); (IΣm, IΣn) for 1 ≤ m < n; (PA, ACA0); (ZFC, ZFC + CH); (ZFC, ZFC + ¬CH) etc. For the case of finitely axiomatized extensions of theories these results are extended to modal logics with propositional constants.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 1 , March 1996 , pp. 91 - 124
Copyright
Copyright © Association for Symbolic Logic 1996

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