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THE MODAL LOGIC OF STONE SPACES: DIAMOND AS DERIVATIVE

Published online by Cambridge University Press:  22 January 2010

GURAM BEZHANISHVILI*
Affiliation:
Department of Mathematical Sciences, New Mexico State University
LEO ESAKIA*
Affiliation:
Department of Mathematical Logic, A. Razmadze Mathematical Institute
DAVID GABELAIA*
Affiliation:
Department of Mathematical Logic, A. Razmadze Mathematical Institute
*
*DEPARTMENT OF MATHEMATICAL SCIENCES, NEW MEXICO STATE UNIVERSITY, LAS CRUCES, NM 88003. E-mail:gbezhani@nmsu.edu
DEPARTMENT OF MATHEMATICAL LOGIC, A. RAZMADZE MATHEMATICAL INSTITUTE, M. ALEKSIDZE STR. 1, TBILISI 0193, GEORGIA. E-mail:esakia@hotmail.com
DEPARTMENT OF MATHEMATICAL LOGIC, A. RAZMADZE MATHEMATICAL INSTITUTE, M. ALEKSIDZE STR. 1, TBILISI 0193, GEORGIA. E-mail:gabelaia@gmail.com

Abstract

We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces is K4 and the modal logic of weakly scattered Stone spaces is K4G. As a corollary, we obtain that K4 is also the modal logic of compact Hausdorff spaces and K4G is the modal logic of weakly scattered compact Hausdorff spaces.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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