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

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