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- W2908142933 abstract "For a topological space X, let L(X) be the modal logic of X where □ is interpreted as interior (and hence ◇ as closure) in X. It was shown in [3] that the modal logics S4, S4.1, S4.2, S4.1.2, S4.Grz, S4.Grzn (n≥1), and their intersections arise as L(X) for some Stone space X. We give an example of a scattered Stone space whose logic is not such an intersection. This gives an affirmative answer to [3, Question 6.2]. On the other hand, we show that a scattered Stone space that is in addition hereditarily paracompact does not give rise to a new logic; namely we show that the logic of such a space is either S4.Grz or S4.Grzn for some n≥1. In fact, we prove this result for any scattered locally compact open hereditarily collectionwise normal and open hereditarily strongly zero-dimensional space." @default.
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- W2908142933 date "2019-05-01" @default.
- W2908142933 modified "2023-09-28" @default.
- W2908142933 title "On modal logics arising from scattered locally compact Hausdorff spaces" @default.
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- W2908142933 doi "https://doi.org/10.1016/j.apal.2018.12.005" @default.
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