The Fixed Point Property in Modal Logic

Abstract

This paper deals with the modal logics associated with (possibly nonstandard) provability predicates of Peano Arithmetic. One of our goals is to present some modal systems having the fixed point property and not extending the Gödel-Löb system GL. We prove that, for every has the explicit fixed point property. Our main result states that every complete modal logic L having the Craig's interpolation property and such that , where and are suitable modal formulas, has the explicit fixed point property

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2010-08-24

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References found in this work

Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.
The Modal Logic of Provability. The Sequential Approach.Giovanni Sambin & Silvio Valentini - 1982 - Journal of Philosophical Logic 11 (3):311 - 342.
Modal Tableau Calculi and Interpolation.Wolfgang Rautenberg - 1983 - Journal of Philosophical Logic 12 (4):403 - 423.

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