## Journal of Symbolic Logic

### Bimodal Logics for Extensions of Arithmetical Theories

Lev D. Beklemishev

#### 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 $(I\Delta_0 + EXP, PRA); (PRA, I\Sigma_1); (I\Sigma_m, I\Sigma_n)$ 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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744929

Mathematical Reviews number (MathSciNet)
MR1380679

Zentralblatt MATH identifier
0858.03024

JSTOR