Bezhanishvili, GuramFernández Duque, David2025-07-252025-07-252024-12-010022-4812https://hdl.handle.net/2445/222594The 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.23 p.application/pdfengcc by (c) Bezhanishvili, Guram et al., 2024http://creativecommons.org/licenses/by/3.0/es/Semàntica (Filosofia)Temps (Lògica)Modalitat (Lògica)Espai (Filosofia)Semantics (Philosophy)Tense (Logic)Modality (Logic)Space (Philosophy)info:eu-repo/semantics/article7434842025-07-25info:eu-repo/semantics/openAccess