Variations of the free implicative semilattice extension of a Hilbert algebra

Autores
Castiglioni, José Luis; San Martín, Hernán Javier
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Celani and Jansana (Math Log Q 58(3):188–207, 2012) give an explicit description of the free implicative semilattice extension of a Hilbert algebra. In this paper, we give an alternative path conducing to this construction. Furthermore, following our procedure, we show that an adjunction can be obtained between the algebraic categories of Hilbert algebras with supremum and that of generalized Heyting algebras. Finally, in the last section, we describe a functor from the algebraic category of Hilbert algebras to that of generalized Heyting algebras, of possible independent interest.
Fil: Castiglioni, José Luis. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: San Martín, Hernán Javier. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Materia
FREE ALGEBRAS
HILBERT ALGEBRAS
IMPLICATIVE SEMILATTICE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/94687
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Variations of the free implicative semilattice extension of a Hilbert algebraCastiglioni, José LuisSan Martín, Hernán JavierFREE ALGEBRASHILBERT ALGEBRASIMPLICATIVE SEMILATTICEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Celani and Jansana (Math Log Q 58(3):188–207, 2012) give an explicit description of the free implicative semilattice extension of a Hilbert algebra. In this paper, we give an alternative path conducing to this construction. Furthermore, following our procedure, we show that an adjunction can be obtained between the algebraic categories of Hilbert algebras with supremum and that of generalized Heyting algebras. Finally, in the last section, we describe a functor from the algebraic category of Hilbert algebras to that of generalized Heyting algebras, of possible independent interest.Fil: Castiglioni, José Luis. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: San Martín, Hernán Javier. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaSpringer Verlag Berlín2019-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/94687Castiglioni, José Luis; San Martín, Hernán Javier; Variations of the free implicative semilattice extension of a Hilbert algebra; Springer Verlag Berlín; Soft Computing; 23; 13; 7-2019; 4633–46411432-76431433-7479CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s00500-018-3426-0info:eu-repo/semantics/altIdentifier/doi/10.1007/s00500-018-3426-0info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1807.02423info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:55:09Zoai:ri.conicet.gov.ar:11336/94687instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:55:09.643CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Variations of the free implicative semilattice extension of a Hilbert algebra
title Variations of the free implicative semilattice extension of a Hilbert algebra
spellingShingle Variations of the free implicative semilattice extension of a Hilbert algebra
Castiglioni, José Luis
FREE ALGEBRAS
HILBERT ALGEBRAS
IMPLICATIVE SEMILATTICE
title_short Variations of the free implicative semilattice extension of a Hilbert algebra
title_full Variations of the free implicative semilattice extension of a Hilbert algebra
title_fullStr Variations of the free implicative semilattice extension of a Hilbert algebra
title_full_unstemmed Variations of the free implicative semilattice extension of a Hilbert algebra
title_sort Variations of the free implicative semilattice extension of a Hilbert algebra
dc.creator.none.fl_str_mv Castiglioni, José Luis
San Martín, Hernán Javier
author Castiglioni, José Luis
author_facet Castiglioni, José Luis
San Martín, Hernán Javier
author_role author
author2 San Martín, Hernán Javier
author2_role author
dc.subject.none.fl_str_mv FREE ALGEBRAS
HILBERT ALGEBRAS
IMPLICATIVE SEMILATTICE
topic FREE ALGEBRAS
HILBERT ALGEBRAS
IMPLICATIVE SEMILATTICE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Celani and Jansana (Math Log Q 58(3):188–207, 2012) give an explicit description of the free implicative semilattice extension of a Hilbert algebra. In this paper, we give an alternative path conducing to this construction. Furthermore, following our procedure, we show that an adjunction can be obtained between the algebraic categories of Hilbert algebras with supremum and that of generalized Heyting algebras. Finally, in the last section, we describe a functor from the algebraic category of Hilbert algebras to that of generalized Heyting algebras, of possible independent interest.
Fil: Castiglioni, José Luis. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: San Martín, Hernán Javier. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
description Celani and Jansana (Math Log Q 58(3):188–207, 2012) give an explicit description of the free implicative semilattice extension of a Hilbert algebra. In this paper, we give an alternative path conducing to this construction. Furthermore, following our procedure, we show that an adjunction can be obtained between the algebraic categories of Hilbert algebras with supremum and that of generalized Heyting algebras. Finally, in the last section, we describe a functor from the algebraic category of Hilbert algebras to that of generalized Heyting algebras, of possible independent interest.
publishDate 2019
dc.date.none.fl_str_mv 2019-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/94687
Castiglioni, José Luis; San Martín, Hernán Javier; Variations of the free implicative semilattice extension of a Hilbert algebra; Springer Verlag Berlín; Soft Computing; 23; 13; 7-2019; 4633–4641
1432-7643
1433-7479
CONICET Digital
CONICET
url http://hdl.handle.net/11336/94687
identifier_str_mv Castiglioni, José Luis; San Martín, Hernán Javier; Variations of the free implicative semilattice extension of a Hilbert algebra; Springer Verlag Berlín; Soft Computing; 23; 13; 7-2019; 4633–4641
1432-7643
1433-7479
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s00500-018-3426-0
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00500-018-3426-0
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1807.02423
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Verlag Berlín
publisher.none.fl_str_mv Springer Verlag Berlín
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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