Algebraic functions in Łukasiewicz implication algebras

Autores
Campercholi, Miguel Alejandro Carlos; Castaño, Diego Nicolás; Díaz Varela, José Patricio
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article we study algebraic functions in {→, 1}-subreducts of MV-algebras, also known as Łukasiewicz implication algebras. A function is algebraic on an algebra A if it is definable by a conjunction of equations on A. We fully characterize algebraic functions on every Łukasiewicz implication algebra belonging to a finitely generated variety. The main tool to accomplish this is a factorization result describing algebraic functions in a subproduct in terms of the algebraic functions of the factors. We prove a global representation theorem for finite Łukasiewicz implication algebras which extends a similar one already known for Tarski algebras. This result together with the knowledge of algebraic functions allowed us to give a partial description of the lattice of classes axiomatized by sentences of the form ∀∃!∧ p ≈ q within the variety generated by the 3-element chain.
Fil: Campercholi, Miguel Alejandro Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Castaño, Diego Nicolás. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Materia
ALGEBRAIC FUNCTIONS
ALGEBRAICALLY EXPANDABLE CLASSES
UKASIEWICZ IMPLICATION ALGEBRAS
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:11336/58361
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Algebraic functions in Łukasiewicz implication algebrasCampercholi, Miguel Alejandro CarlosCastaño, Diego NicolásDíaz Varela, José PatricioALGEBRAIC FUNCTIONSALGEBRAICALLY EXPANDABLE CLASSESUKASIEWICZ IMPLICATION ALGEBRAShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article we study algebraic functions in {→, 1}-subreducts of MV-algebras, also known as Łukasiewicz implication algebras. A function is algebraic on an algebra A if it is definable by a conjunction of equations on A. We fully characterize algebraic functions on every Łukasiewicz implication algebra belonging to a finitely generated variety. The main tool to accomplish this is a factorization result describing algebraic functions in a subproduct in terms of the algebraic functions of the factors. We prove a global representation theorem for finite Łukasiewicz implication algebras which extends a similar one already known for Tarski algebras. This result together with the knowledge of algebraic functions allowed us to give a partial description of the lattice of classes axiomatized by sentences of the form ∀∃!∧ p ≈ q within the variety generated by the 3-element chain.Fil: Campercholi, Miguel Alejandro Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Castaño, Diego Nicolás. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaWorld Scientific2016-03info: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/11336/58361Campercholi, Miguel Alejandro Carlos; Castaño, Diego Nicolás; Díaz Varela, José Patricio; Algebraic functions in Łukasiewicz implication algebras; World Scientific; International Journal of Algebra and Computation; 26; 2; 3-2016; 223-2470218-1967CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218196716500119info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218196716500119info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:01:02Zoai:ri.conicet.gov.ar:11336/58361instacron: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 10:01:02.983CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Algebraic functions in Łukasiewicz implication algebras
title Algebraic functions in Łukasiewicz implication algebras
spellingShingle Algebraic functions in Łukasiewicz implication algebras
Campercholi, Miguel Alejandro Carlos
ALGEBRAIC FUNCTIONS
ALGEBRAICALLY EXPANDABLE CLASSES
UKASIEWICZ IMPLICATION ALGEBRAS
title_short Algebraic functions in Łukasiewicz implication algebras
title_full Algebraic functions in Łukasiewicz implication algebras
title_fullStr Algebraic functions in Łukasiewicz implication algebras
title_full_unstemmed Algebraic functions in Łukasiewicz implication algebras
title_sort Algebraic functions in Łukasiewicz implication algebras
dc.creator.none.fl_str_mv Campercholi, Miguel Alejandro Carlos
Castaño, Diego Nicolás
Díaz Varela, José Patricio
author Campercholi, Miguel Alejandro Carlos
author_facet Campercholi, Miguel Alejandro Carlos
Castaño, Diego Nicolás
Díaz Varela, José Patricio
author_role author
author2 Castaño, Diego Nicolás
Díaz Varela, José Patricio
author2_role author
author
dc.subject.none.fl_str_mv ALGEBRAIC FUNCTIONS
ALGEBRAICALLY EXPANDABLE CLASSES
UKASIEWICZ IMPLICATION ALGEBRAS
topic ALGEBRAIC FUNCTIONS
ALGEBRAICALLY EXPANDABLE CLASSES
UKASIEWICZ IMPLICATION ALGEBRAS
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 article we study algebraic functions in {→, 1}-subreducts of MV-algebras, also known as Łukasiewicz implication algebras. A function is algebraic on an algebra A if it is definable by a conjunction of equations on A. We fully characterize algebraic functions on every Łukasiewicz implication algebra belonging to a finitely generated variety. The main tool to accomplish this is a factorization result describing algebraic functions in a subproduct in terms of the algebraic functions of the factors. We prove a global representation theorem for finite Łukasiewicz implication algebras which extends a similar one already known for Tarski algebras. This result together with the knowledge of algebraic functions allowed us to give a partial description of the lattice of classes axiomatized by sentences of the form ∀∃!∧ p ≈ q within the variety generated by the 3-element chain.
Fil: Campercholi, Miguel Alejandro Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Castaño, Diego Nicolás. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
description In this article we study algebraic functions in {→, 1}-subreducts of MV-algebras, also known as Łukasiewicz implication algebras. A function is algebraic on an algebra A if it is definable by a conjunction of equations on A. We fully characterize algebraic functions on every Łukasiewicz implication algebra belonging to a finitely generated variety. The main tool to accomplish this is a factorization result describing algebraic functions in a subproduct in terms of the algebraic functions of the factors. We prove a global representation theorem for finite Łukasiewicz implication algebras which extends a similar one already known for Tarski algebras. This result together with the knowledge of algebraic functions allowed us to give a partial description of the lattice of classes axiomatized by sentences of the form ∀∃!∧ p ≈ q within the variety generated by the 3-element chain.
publishDate 2016
dc.date.none.fl_str_mv 2016-03
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/11336/58361
Campercholi, Miguel Alejandro Carlos; Castaño, Diego Nicolás; Díaz Varela, José Patricio; Algebraic functions in Łukasiewicz implication algebras; World Scientific; International Journal of Algebra and Computation; 26; 2; 3-2016; 223-247
0218-1967
CONICET Digital
CONICET
url http://hdl.handle.net/11336/58361
identifier_str_mv Campercholi, Miguel Alejandro Carlos; Castaño, Diego Nicolás; Díaz Varela, José Patricio; Algebraic functions in Łukasiewicz implication algebras; World Scientific; International Journal of Algebra and Computation; 26; 2; 3-2016; 223-247
0218-1967
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218196716500119
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218196716500119
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 World Scientific
publisher.none.fl_str_mv World Scientific
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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