The modal logic of stone spaces: Diamond as derivative

Review of Symbolic Logic 3 (1):26-40 (2010)
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.
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DOI 10.1017/S1755020309990335
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Leo Esakia (2004). Intuitionistic Logic and Modality Via Topology. Annals of Pure and Applied Logic 127 (1-3):155-170.

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Daniele Mundici (1998). Foreword. Studia Logica 61 (1):1-1.

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