# MoL-2006-08: Axiomatization of ML and Cheq

MoL-2006-08: Fontaine, Gaëlle (2006) Axiomatization of ML and Cheq. [Report]

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## Abstract

In this thesis we investigate the connection between two intermediate logics: Medvedev's logic and the logic of chequered subsets. The former has been introduced by Medvedev in the sixties as a a logic of finite problems and the later, by van Benthem, Bezhanishvili and Gehrke in 2003 as a spatial logic of the chequered subsets of R^\infty. Litak (2004) conjectured that these two logics are closely related; in particular, that Medvedev's logic is finitely axiomatizable over thelogic of chequered subsets. In this thesis we refute Litak's conjecture by showing that Medvedev's logic is not finitely axiomatizable over the logic of chequered subsets. We also reproduce the original proof of Maksimova, Shehtman and Skvorcov (1978) that Medvedev's logic is not finitely axiomatizable and prove that the logic of chequered subsets is not axiomatizable with four variables.

Item Type: Report MoL-2006-08 Master of Logic Thesis (MoL) Series 2006 12 Oct 2016 14:38 12 Oct 2016 14:38 https://eprints.illc.uva.nl/id/eprint/771