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On fragments of Medvedev's logic

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Abstract

Medvedev's intermediate logic (MV) can be defined by means of Kripke semantics as the family of Kripke frames given by finite Boolean algebras without units as partially ordered sets. The aim of this paper is to present a proof of the theorem: For every set of connectivesΦ such that\(\{ \to , \vee , \urcorner \} \not \subseteq \Phi \subseteq \{ \to , \wedge , \urcorner \} \) theΦ-fragment ofMV equals theΦ fragment of intuitionistic logic. The final part of the paper brings the negative solution to the problem set forth by T. Hosoi and H. Ono, namely: is an intermediate logic based on the axiom (⌝a→b∨c) →(⌉a→b)∨(⌝a → c) separable?

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The author is much obliged to Professor Andrzej Wroński for his precious suggestions which were of great help in writing this paper.

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Szatkowski, M. On fragments of Medvedev's logic. Stud Logica 40, 39–54 (1981). https://doi.org/10.1007/BF01837554

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  • DOI: https://doi.org/10.1007/BF01837554

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