Modal counterparts of Medvedev logic of finite problems are not finitely axiomatizable

Studia Logica 49 (3):365 - 385 (1990)
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Abstract

We consider modal logics whose intermediate fragments lie between the logic of infinite problems [20] and the Medvedev logic of finite problems [15]. There is continuum of such logics [19]. We prove that none of them is finitely axiomatizable. The proof is based on methods from [12] and makes use of some graph-theoretic constructions (operations on coverings, and colourings).

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Valentin Shehtman
Moscow State University

References found in this work

An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
An incomplete logic containing S.Kit Fine - 1974 - Theoria 40 (1):23-29.
One hundred and two problems in mathematical logic.Harvey Friedman - 1975 - Journal of Symbolic Logic 40 (2):113-129.
An ascending chain of S4 logics.Kit Fine - 1974 - Theoria 40 (2):110-116.

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