Short notes

The lattice of extensions of the modal logic of two equivalence relations has the cardinality of the continuum

M. M. Izmailov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A continuum of different modal logics over $S5 \otimes S5$ is constructed in the paper, which proves that the capacity of the lattice of all normal extensions of the logic of two equivalence relations $\operatorname{Ext}(S5\otimes S5)$ is a continuum.

Key words: modal logic, fusion of logics, extensions of logics, logic of equivalence relation.

UDC: 510.6

Received: 05.04.2010

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