Journal of Symbolic Logic 61 (1):91-124 (1996)

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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 (IΔ 0 + EXP, PRA); (PRA, IΣ 1 ); (IΣ m , IΣ n ) for $1 \leq m etc. For the case of finitely axiomatized extensions of theories these results are extended to modal logics with propositional constants
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DOI 10.2307/2275600
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References found in this work BETA

On the Scheme of Induction for Bounded Arithmetic Formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (3):261-302.
Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems.G. Kreisel & A. Lévy - 1968 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 14 (7-12):97-142.
Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems.Georg Kreisel & Azriel Lévy - 1968 - Zeitschrift für Mathematische Logic Und Grundlagen der Mathematik 14 (1):97--142.
Fragments of Arithmetic.Wilfried Sieg - 1985 - Annals of Pure and Applied Logic 28 (1):33-71.
The Logic of Provability.Philip Scowcroft - 1995 - Philosophical Review 104 (4):627.

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Citations of this work BETA

Iterated Local Reflection Versus Iterated Consistency.Lev Beklemishev - 1995 - Annals of Pure and Applied Logic 75 (1-2):25-48.
Provability Logic.Rineke Verbrugge - 2008 - Stanford Encyclopedia of Philosophy.

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