Semi-Heyting Algebras Term-equivalent to Gödel Algebras

Autores
Abad, Manuel; Cornejo, Juan Manuel; Díaz Varela, José Patricio
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we investigate those subvarieties of the variety SH of semi-Heyting algebras which are term-equivalent to the variety LH of Gödel algebras (linear Heyting algebras). We prove that the only other subvarieties with this property are the variety LCom of commutative semi-Heyting algebras and the variety L∨ generated by the chains in which a < b implies a → b = b. We also study the variety C generated within SH by LH, L∨ and LCom. In particular we prove that C is locally finite and we obtain a construction of the finitely generated free algebra in C.
Fil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Cornejo, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Materia
Heyting Algebra
Linear Heyting Algebra
Semi-Heyting Algebra
Term-Equivalent Varieties
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/11864
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/11864
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Semi-Heyting Algebras Term-equivalent to Gödel AlgebrasAbad, ManuelCornejo, Juan ManuelDíaz Varela, José PatricioHeyting AlgebraLinear Heyting AlgebraSemi-Heyting AlgebraTerm-Equivalent Varietieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we investigate those subvarieties of the variety SH of semi-Heyting algebras which are term-equivalent to the variety LH of Gödel algebras (linear Heyting algebras). We prove that the only other subvarieties with this property are the variety LCom of commutative semi-Heyting algebras and the variety L∨ generated by the chains in which a < b implies a → b = b. We also study the variety C generated within SH by LH, L∨ and LCom. In particular we prove that C is locally finite and we obtain a construction of the finitely generated free algebra in C.Fil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Cornejo, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaSpringer2013-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/11864Abad, Manuel; Cornejo, Juan Manuel; Díaz Varela, José Patricio; Semi-Heyting Algebras Term-equivalent to Gödel Algebras; Springer; Order; 30; 2; 7-2013; 625-6420167-8094enginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs11083-012-9266-0info:eu-repo/semantics/altIdentifier/doi/10.1007/s11083-012-9266-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:16:36Zoai:ri.conicet.gov.ar:11336/11864instacron: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:34982025-09-29 10:16:36.802CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Semi-Heyting Algebras Term-equivalent to Gödel Algebras
title Semi-Heyting Algebras Term-equivalent to Gödel Algebras
spellingShingle Semi-Heyting Algebras Term-equivalent to Gödel Algebras
Abad, Manuel
Heyting Algebra
Linear Heyting Algebra
Semi-Heyting Algebra
Term-Equivalent Varieties
title_short Semi-Heyting Algebras Term-equivalent to Gödel Algebras
title_full Semi-Heyting Algebras Term-equivalent to Gödel Algebras
title_fullStr Semi-Heyting Algebras Term-equivalent to Gödel Algebras
title_full_unstemmed Semi-Heyting Algebras Term-equivalent to Gödel Algebras
title_sort Semi-Heyting Algebras Term-equivalent to Gödel Algebras
dc.creator.none.fl_str_mv Abad, Manuel
Cornejo, Juan Manuel
Díaz Varela, José Patricio
author Abad, Manuel
author_facet Abad, Manuel
Cornejo, Juan Manuel
Díaz Varela, José Patricio
author_role author
author2 Cornejo, Juan Manuel
Díaz Varela, José Patricio
author2_role author
author
dc.subject.none.fl_str_mv Heyting Algebra
Linear Heyting Algebra
Semi-Heyting Algebra
Term-Equivalent Varieties
topic Heyting Algebra
Linear Heyting Algebra
Semi-Heyting Algebra
Term-Equivalent Varieties
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we investigate those subvarieties of the variety SH of semi-Heyting algebras which are term-equivalent to the variety LH of Gödel algebras (linear Heyting algebras). We prove that the only other subvarieties with this property are the variety LCom of commutative semi-Heyting algebras and the variety L∨ generated by the chains in which a < b implies a → b = b. We also study the variety C generated within SH by LH, L∨ and LCom. In particular we prove that C is locally finite and we obtain a construction of the finitely generated free algebra in C.
Fil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Cornejo, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
description In this paper we investigate those subvarieties of the variety SH of semi-Heyting algebras which are term-equivalent to the variety LH of Gödel algebras (linear Heyting algebras). We prove that the only other subvarieties with this property are the variety LCom of commutative semi-Heyting algebras and the variety L∨ generated by the chains in which a < b implies a → b = b. We also study the variety C generated within SH by LH, L∨ and LCom. In particular we prove that C is locally finite and we obtain a construction of the finitely generated free algebra in C.
publishDate 2013
dc.date.none.fl_str_mv 2013-07
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/11336/11864
Abad, Manuel; Cornejo, Juan Manuel; Díaz Varela, José Patricio; Semi-Heyting Algebras Term-equivalent to Gödel Algebras; Springer; Order; 30; 2; 7-2013; 625-642
0167-8094
url http://hdl.handle.net/11336/11864
identifier_str_mv Abad, Manuel; Cornejo, Juan Manuel; Díaz Varela, José Patricio; Semi-Heyting Algebras Term-equivalent to Gödel Algebras; Springer; Order; 30; 2; 7-2013; 625-642
0167-8094
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/article/10.1007%2Fs11083-012-9266-0
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11083-012-9266-0
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.070432

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