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THE MODAL LOGIC OF STONE SPACES: DIAMOND AS DERIVATIVE

Published online by Cambridge University Press:  22 January 2010

GURAM BEZHANISHVILI ,
LEO ESAKIA  and
DAVID GABELAIA
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:[email protected]
†DEPARTMENT OF MATHEMATICAL LOGIC, A. RAZMADZE MATHEMATICAL INSTITUTE, M. ALEKSIDZE STR. 1, TBILISI 0193, GEORGIA. E-mail:[email protected]
‡DEPARTMENT OF MATHEMATICAL LOGIC, A. RAZMADZE MATHEMATICAL INSTITUTE, M. ALEKSIDZE STR. 1, TBILISI 0193, GEORGIA. E-mail:[email protected]
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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
Information
The Review of Symbolic Logic , Volume 3 , Issue 1 , March 2010 , pp. 26 - 40
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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