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- W4287823266 abstract "A topological space is emph{hereditarily $k$-irresolvable} if none of its subspaces can be partitioned into $k$ dense subsets, We use this notion to provide a topological semantics for a sequence of modal logics whose $n$-th member K4$mathbb{C}_n$ is characterised by validity in transitive Kripke frames of circumference at most $n$. We show that under the interpretation of the modality $Diamond$ as the derived set (of limit points) operation, K4$mathbb{C}_n$ is characterised by validity in all spaces that are hereditarily $n+1$-irresolvable and have the T$_D$ separation property. We also identify the extensions of K4$mathbb{C}_n$ that result when the class of spaces involved is restricted to those that are weakly scattered, or crowded, or openly irresolvable, the latter meaning that every non-empty open subspace is 2-irresolvable. Finally we give a topological semantics for K4M, where M is the McKinsey axiom." @default.
- W4287823266 created "2022-07-26" @default.
- W4287823266 creator A5037638170 @default.
- W4287823266 date "2020-03-29" @default.
- W4287823266 modified "2023-10-18" @default.
- W4287823266 title "Modal Logics of Some Hereditarily Irresolvable Spaces" @default.
- W4287823266 doi "https://doi.org/10.48550/arxiv.2003.12946" @default.
- W4287823266 hasPublicationYear "2020" @default.
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