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2024-12-01

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cc by (c) Bezhanishvili, Guram et al., 2024
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/222594

The Baire closure and its logic

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https://doi.org/10.1017/jsl.2024.1

Abstract

The Baire algebra of a topological space X is the quotient of the algebra of all subsets of X modulo the meager sets. We show that this Boolean algebra can be endowed with a natural closure operator, resulting in a closure algebra which we denote Baire(X ). We identify the modal logic of such algebras to be the well-known system S5, and prove soundness and strong completeness for the cases where X is crowded and either completely metrizable and continuum-sized or locally compact Hausdorff. We also show that every extension of S5 is the modal logic of a subalgebra of Baire(X ), and that soundness and strong completeness also holds in the language with the universal modality.

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Semàntica (Filosofia), Temps (Lògica), Modalitat (Lògica), Espai (Filosofia)

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Semantics (Philosophy), Tense (Logic), Modality (Logic), Space (Philosophy)

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BEZHANISHVILI, Guram and FERNÁNDEZ DUQUE, David. The Baire closure and its logic. Journal of Symbolic Logic. 2024. ISSN 0022-4812. [consulted: 18 of June of 2026]. Available at: https://hdl.handle.net/2445/222594

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