The Baire closure and its logic

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 algebr...

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Autores: Bezhanishvili, Guram, Fernández Duque, David
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/222594
Acceso en línea:https://hdl.handle.net/2445/222594
Access Level:acceso abierto
Palabra clave:Semàntica (Filosofia)
Temps (Lògica)
Modalitat (Lògica)
Espai (Filosofia)
Semantics (Philosophy)
Tense (Logic)
Modality (Logic)
Space (Philosophy)
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spelling The Baire closure and its logicBezhanishvili, GuramFernández Duque, DavidSemàntica (Filosofia)Temps (Lògica)Modalitat (Lògica)Espai (Filosofia)Semantics (Philosophy)Tense (Logic)Modality (Logic)Space (Philosophy)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.Association for Symbolic Logic2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/222594Articles publicats en revistes (Filosofia)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/10.1017/jsl.2024.1Journal of Symbolic Logic, 2024https://doi.org/10.1017/jsl.2024.1cc by (c) Bezhanishvili, Guram et al., 2024http://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2225942026-05-27T06:46:51Z
dc.title.none.fl_str_mv The Baire closure and its logic
title The Baire closure and its logic
spellingShingle The Baire closure and its logic
Bezhanishvili, Guram
Semàntica (Filosofia)
Temps (Lògica)
Modalitat (Lògica)
Espai (Filosofia)
Semantics (Philosophy)
Tense (Logic)
Modality (Logic)
Space (Philosophy)
title_short The Baire closure and its logic
title_full The Baire closure and its logic
title_fullStr The Baire closure and its logic
title_full_unstemmed The Baire closure and its logic
title_sort The Baire closure and its logic
dc.creator.none.fl_str_mv Bezhanishvili, Guram
Fernández Duque, David
author Bezhanishvili, Guram
author_facet Bezhanishvili, Guram
Fernández Duque, David
author_role author
author2 Fernández Duque, David
author2_role author
dc.subject.none.fl_str_mv Semàntica (Filosofia)
Temps (Lògica)
Modalitat (Lògica)
Espai (Filosofia)
Semantics (Philosophy)
Tense (Logic)
Modality (Logic)
Space (Philosophy)
topic Semàntica (Filosofia)
Temps (Lògica)
Modalitat (Lògica)
Espai (Filosofia)
Semantics (Philosophy)
Tense (Logic)
Modality (Logic)
Space (Philosophy)
description 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.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/222594
url https://hdl.handle.net/2445/222594
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1017/jsl.2024.1
Journal of Symbolic Logic, 2024
https://doi.org/10.1017/jsl.2024.1
dc.rights.none.fl_str_mv cc by (c) Bezhanishvili, Guram et al., 2024
http://creativecommons.org/licenses/by/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by (c) Bezhanishvili, Guram et al., 2024
http://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Association for Symbolic Logic
publisher.none.fl_str_mv Association for Symbolic Logic
dc.source.none.fl_str_mv Articles publicats en revistes (Filosofia)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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