On some Classes of Heyting Algebras with Successor that have the Amalgamation Property

Autores
Castiglioni, José Luis; San Martín, Hernán Javier
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we shall prove that certain subvarieties of the variety of Salgebras (Heyting algebras with successor) has amalgamation. This result together with an appropriate version of Theorem 1 of [L. L. Maksimova, Craig’s theorem in superintuitionistic logics and amalgamable varieties of pseudo-boolean algebras, Algebra i Logika, 16(6):643-681, 1977] allows us to show interpolation in the calculus IPC S (n), associated with these varieties. We use that every algebra in any of the varieties of S-algebras studied in this work has a canonical extension, to show completeness of the calculus IPC S (n) with respect to appropriate Kripke models.
Facultad de Ciencias Exactas
Materia
Matemática
Amalgamation property
Craig’s interpolation theorem
Heyting algebras with operators
Extensions of intuitionistic propositional calculus
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/146211
Acceder
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network_name_str SEDICI (UNLP)
spelling On some Classes of Heyting Algebras with Successor that have the Amalgamation PropertyCastiglioni, José LuisSan Martín, Hernán JavierMatemáticaAmalgamation propertyCraig’s interpolation theoremHeyting algebras with operatorsExtensions of intuitionistic propositional calculusIn this paper we shall prove that certain subvarieties of the variety of Salgebras (Heyting algebras with successor) has amalgamation. This result together with an appropriate version of Theorem 1 of [L. L. Maksimova, Craig’s theorem in superintuitionistic logics and amalgamable varieties of pseudo-boolean algebras, Algebra i Logika, 16(6):643-681, 1977] allows us to show interpolation in the calculus IPC S (n), associated with these varieties. We use that every algebra in any of the varieties of S-algebras studied in this work has a canonical extension, to show completeness of the calculus IPC S (n) with respect to appropriate Kripke models.Facultad de Ciencias Exactas2012-10-20info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1255-1269http://sedici.unlp.edu.ar/handle/10915/146211enginfo:eu-repo/semantics/altIdentifier/issn/0039-3215info:eu-repo/semantics/altIdentifier/issn/1572-8730info:eu-repo/semantics/altIdentifier/doi/10.1007/s11225-012-9451-6info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T11:04:38Zoai:sedici.unlp.edu.ar:10915/146211Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 11:04:38.343SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
title On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
spellingShingle On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
Castiglioni, José Luis
Matemática
Amalgamation property
Craig’s interpolation theorem
Heyting algebras with operators
Extensions of intuitionistic propositional calculus
title_short On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
title_full On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
title_fullStr On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
title_full_unstemmed On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
title_sort On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
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 Matemática
Amalgamation property
Craig’s interpolation theorem
Heyting algebras with operators
Extensions of intuitionistic propositional calculus
topic Matemática
Amalgamation property
Craig’s interpolation theorem
Heyting algebras with operators
Extensions of intuitionistic propositional calculus
dc.description.none.fl_txt_mv In this paper we shall prove that certain subvarieties of the variety of Salgebras (Heyting algebras with successor) has amalgamation. This result together with an appropriate version of Theorem 1 of [L. L. Maksimova, Craig’s theorem in superintuitionistic logics and amalgamable varieties of pseudo-boolean algebras, Algebra i Logika, 16(6):643-681, 1977] allows us to show interpolation in the calculus IPC S (n), associated with these varieties. We use that every algebra in any of the varieties of S-algebras studied in this work has a canonical extension, to show completeness of the calculus IPC S (n) with respect to appropriate Kripke models.
Facultad de Ciencias Exactas
description In this paper we shall prove that certain subvarieties of the variety of Salgebras (Heyting algebras with successor) has amalgamation. This result together with an appropriate version of Theorem 1 of [L. L. Maksimova, Craig’s theorem in superintuitionistic logics and amalgamable varieties of pseudo-boolean algebras, Algebra i Logika, 16(6):643-681, 1977] allows us to show interpolation in the calculus IPC S (n), associated with these varieties. We use that every algebra in any of the varieties of S-algebras studied in this work has a canonical extension, to show completeness of the calculus IPC S (n) with respect to appropriate Kripke models.
publishDate 2012
dc.date.none.fl_str_mv 2012-10-20
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info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/146211
url http://sedici.unlp.edu.ar/handle/10915/146211
dc.language.none.fl_str_mv eng
language eng
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info:eu-repo/semantics/altIdentifier/issn/1572-8730
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11225-012-9451-6
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
1255-1269
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
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reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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