a1 Department of Mathematical Sciences, New Mexico State University
a2 Department of Mathematical Logic, A. Razmadze Mathematical Institute
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.
(Received January 28 2009)