On structural completeness versus almost structural completeness problem : a discriminator varieties case study

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We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varie...

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Autores principales:	Campercholi, Miguel Alejandro Carlos, Stronkowski, Michal M., Vaggione, Diego José
Formato:	submittedVersion Fil: Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Fil: Stronkowski, Michal M. Warsaw University of Technology. Faculty of Mathematics and Information Sciences; Polonia. Fil: Fil: Vaggione, Diego José. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. article
Lenguaje:	Inglés
Publicado:	2021
Materias:	Structural completeness Almost structural completeness Discriminator varieties Semisimple quasivarieties Minimal varieties Minimal quasivarieties
Acceso en línea:	http://hdl.handle.net/11086/20551 https://doi.org/10.1093/jigpal/jzu032
Aporte de:	Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba

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spelling	I10-R141-11086-205512023-05-22T18:52:47Z On structural completeness versus almost structural completeness problem : a discriminator varieties case study Campercholi, Miguel Alejandro Carlos Stronkowski, Michal M. Vaggione, Diego José Structural completeness Almost structural completeness Discriminator varieties Semisimple quasivarieties Minimal varieties Minimal quasivarieties submittedVersion Fil: Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Fil: Stronkowski, Michal M. Warsaw University of Technology. Faculty of Mathematics and Information Sciences; Polonia. Fil: Fil: Vaggione, Diego José. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that L has an adequate semantics given by a discriminator variety. Then L is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete. submittedVersion Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Stronkowski, Michal M. Warsaw University of Technology. Faculty of Mathematics and Information Sciences; Polonia. Fil: Vaggione, Diego José. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Matemática Pura 2021-10-01T16:30:00Z 2021-10-01T16:30:00Z 2015 article Campercholi, M., Stronkowski, M. y Vaggione, D. (2015). On structural completeness versus almost structural completeness problem. [versión enviada para evaluación] ( Publicada posteriormente en Logic Journal of the Interest Group in Pure and Applied Logic, 23 (2), 235-246. https://doi.org/10.1093/jigpal/jzu032 ) http://hdl.handle.net/11086/20551 https://doi.org/10.1093/jigpal/jzu032 eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ Impreso; Electrónico y/o Digital ISSN 1367-0751
institution	Universidad Nacional de Córdoba
institution_str	I-10
repository_str	R-141
collection	Repositorio Digital Universitario (UNC)
language	Inglés
topic	Structural completeness Almost structural completeness Discriminator varieties Semisimple quasivarieties Minimal varieties Minimal quasivarieties
spellingShingle	Structural completeness Almost structural completeness Discriminator varieties Semisimple quasivarieties Minimal varieties Minimal quasivarieties Campercholi, Miguel Alejandro Carlos Stronkowski, Michal M. Vaggione, Diego José On structural completeness versus almost structural completeness problem : a discriminator varieties case study
topic_facet	Structural completeness Almost structural completeness Discriminator varieties Semisimple quasivarieties Minimal varieties Minimal quasivarieties
description	We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that L has an adequate semantics given by a discriminator variety. Then L is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete.
format	submittedVersion Fil: Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Fil: Stronkowski, Michal M. Warsaw University of Technology. Faculty of Mathematics and Information Sciences; Polonia. Fil: Fil: Vaggione, Diego José. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. article
author	Campercholi, Miguel Alejandro Carlos Stronkowski, Michal M. Vaggione, Diego José
author_facet	Campercholi, Miguel Alejandro Carlos Stronkowski, Michal M. Vaggione, Diego José
author_sort	Campercholi, Miguel Alejandro Carlos
title	On structural completeness versus almost structural completeness problem : a discriminator varieties case study
title_short	On structural completeness versus almost structural completeness problem : a discriminator varieties case study
title_full	On structural completeness versus almost structural completeness problem : a discriminator varieties case study
title_fullStr	On structural completeness versus almost structural completeness problem : a discriminator varieties case study
title_full_unstemmed	On structural completeness versus almost structural completeness problem : a discriminator varieties case study
title_sort	on structural completeness versus almost structural completeness problem : a discriminator varieties case study
publishDate	2021
url	http://hdl.handle.net/11086/20551 https://doi.org/10.1093/jigpal/jzu032
work_keys_str_mv	AT campercholimiguelalejandrocarlos onstructuralcompletenessversusalmoststructuralcompletenessproblemadiscriminatorvarietiescasestudy AT stronkowskimichalm onstructuralcompletenessversusalmoststructuralcompletenessproblemadiscriminatorvarietiescasestudy AT vaggionediegojose onstructuralcompletenessversusalmoststructuralcompletenessproblemadiscriminatorvarietiescasestudy
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On structural completeness versus almost structural completeness problem : a discriminator varieties case study

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