On the variety of Heyting algebras with successor generated by all finite chains
- Autores
- Castiglioni, José Luis; San Martín, Hernán Javier
- Año de publicación
- 2010
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Contrary to the variety of Heyting algebras, finite Heyting algebras with successor only generate a proper subvariety of that of all Heyting algebras with successor. In particular, all finite chains generate a proper subvariety, SLHω, of the latter. There is a categorical duality between Heyting algebras with successor and certain Priestley spaces. Let X be the Heyting space associated by this duality to the Heyting algebra with successor H. If there is an ordinal κ and a filtration on X such that X = S λ≤κ Xλ, the height of X is the minimun ordinal ξ ≤ κ such that Xc ξ = ∅. In this case, we also say that H has height ξ. This filtration allows us to write the space X as a disjoint union of antichains. We may think that these antichains define levels on this space. We study the way of characterize subalgebras and homomorphic images in finite Heyting algebras with successor by means of their Priestley spaces. We also depict the spaces associated to the free algebras in various subcategories of SLH.
Fil: Castiglioni, José Luis. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: San Martín, Hernán Javier. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina - Materia
-
SUCCESSOR
CHAINS
FREE
REPRESENTATION - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/125551
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On the variety of Heyting algebras with successor generated by all finite chainsCastiglioni, José LuisSan Martín, Hernán JavierSUCCESSORCHAINSFREEREPRESENTATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Contrary to the variety of Heyting algebras, finite Heyting algebras with successor only generate a proper subvariety of that of all Heyting algebras with successor. In particular, all finite chains generate a proper subvariety, SLHω, of the latter. There is a categorical duality between Heyting algebras with successor and certain Priestley spaces. Let X be the Heyting space associated by this duality to the Heyting algebra with successor H. If there is an ordinal κ and a filtration on X such that X = S λ≤κ Xλ, the height of X is the minimun ordinal ξ ≤ κ such that Xc ξ = ∅. In this case, we also say that H has height ξ. This filtration allows us to write the space X as a disjoint union of antichains. We may think that these antichains define levels on this space. We study the way of characterize subalgebras and homomorphic images in finite Heyting algebras with successor by means of their Priestley spaces. We also depict the spaces associated to the free algebras in various subcategories of SLH.Fil: Castiglioni, José Luis. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: San Martín, Hernán Javier. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaJagiellonian University Press2010-03info: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/11336/125551Castiglioni, José Luis; San Martín, Hernán Javier; On the variety of Heyting algebras with successor generated by all finite chains; Jagiellonian University Press; Reports on Mathematical Logic; 45; 3-2010; 225-2480137-2904CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://ejournals.eu/sj/index.php/rml/article/view/2871info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:40:40Zoai:ri.conicet.gov.ar:11336/125551instacron: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 09:40:40.3CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
On the variety of Heyting algebras with successor generated by all finite chains |
| title |
On the variety of Heyting algebras with successor generated by all finite chains |
| spellingShingle |
On the variety of Heyting algebras with successor generated by all finite chains Castiglioni, José Luis SUCCESSOR CHAINS FREE REPRESENTATION |
| title_short |
On the variety of Heyting algebras with successor generated by all finite chains |
| title_full |
On the variety of Heyting algebras with successor generated by all finite chains |
| title_fullStr |
On the variety of Heyting algebras with successor generated by all finite chains |
| title_full_unstemmed |
On the variety of Heyting algebras with successor generated by all finite chains |
| title_sort |
On the variety of Heyting algebras with successor generated by all finite chains |
| 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 |
SUCCESSOR CHAINS FREE REPRESENTATION |
| topic |
SUCCESSOR CHAINS FREE REPRESENTATION |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
Contrary to the variety of Heyting algebras, finite Heyting algebras with successor only generate a proper subvariety of that of all Heyting algebras with successor. In particular, all finite chains generate a proper subvariety, SLHω, of the latter. There is a categorical duality between Heyting algebras with successor and certain Priestley spaces. Let X be the Heyting space associated by this duality to the Heyting algebra with successor H. If there is an ordinal κ and a filtration on X such that X = S λ≤κ Xλ, the height of X is the minimun ordinal ξ ≤ κ such that Xc ξ = ∅. In this case, we also say that H has height ξ. This filtration allows us to write the space X as a disjoint union of antichains. We may think that these antichains define levels on this space. We study the way of characterize subalgebras and homomorphic images in finite Heyting algebras with successor by means of their Priestley spaces. We also depict the spaces associated to the free algebras in various subcategories of SLH. Fil: Castiglioni, José Luis. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina Fil: San Martín, Hernán Javier. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina |
| description |
Contrary to the variety of Heyting algebras, finite Heyting algebras with successor only generate a proper subvariety of that of all Heyting algebras with successor. In particular, all finite chains generate a proper subvariety, SLHω, of the latter. There is a categorical duality between Heyting algebras with successor and certain Priestley spaces. Let X be the Heyting space associated by this duality to the Heyting algebra with successor H. If there is an ordinal κ and a filtration on X such that X = S λ≤κ Xλ, the height of X is the minimun ordinal ξ ≤ κ such that Xc ξ = ∅. In this case, we also say that H has height ξ. This filtration allows us to write the space X as a disjoint union of antichains. We may think that these antichains define levels on this space. We study the way of characterize subalgebras and homomorphic images in finite Heyting algebras with successor by means of their Priestley spaces. We also depict the spaces associated to the free algebras in various subcategories of SLH. |
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2010 |
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2010-03 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://hdl.handle.net/11336/125551 Castiglioni, José Luis; San Martín, Hernán Javier; On the variety of Heyting algebras with successor generated by all finite chains; Jagiellonian University Press; Reports on Mathematical Logic; 45; 3-2010; 225-248 0137-2904 CONICET Digital CONICET |
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http://hdl.handle.net/11336/125551 |
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Castiglioni, José Luis; San Martín, Hernán Javier; On the variety of Heyting algebras with successor generated by all finite chains; Jagiellonian University Press; Reports on Mathematical Logic; 45; 3-2010; 225-248 0137-2904 CONICET Digital CONICET |
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eng |
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eng |
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