Frontal operators in weak Heyting algebras

In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving nite meets which also satis es the equation τ...

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Autores principales: Celani, Sergio A., San Martín, Hernán Javier
Formato: Articulo
Lenguaje:Inglés
Publicado: 2012
Materias:
Matemática
modal operators
frontal operators
weak Heyting algebras
Priestley duality
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/114720
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-114720
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
modal operators
frontal operators
weak Heyting algebras
Priestley duality
spellingShingle Matemática
modal operators
frontal operators
weak Heyting algebras
Priestley duality
Celani, Sergio A.
San Martín, Hernán Javier
Frontal operators in weak Heyting algebras
topic_facet Matemática
modal operators
frontal operators
weak Heyting algebras
Priestley duality
description In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving nite meets which also satis es the equation τ (a) ≤ b ∨ (b → a), for all a; b ∈ A. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia in [10]. We will study frontal operators in weak Heyting algebras and we will consider two examples of them. We will give a Priestley duality for the category of frontal weak Heyting algebras in terms of relational spaces ⟨X;≤; T;R⟩ where ⟨X;≤; T⟩ is a WH- space [6], and R is an additional binary relation used to interpret the modal operator. We will also study the WH-algebras with successor and the WH-algebras with gamma. For these varieties we will give two topological dualities. The rst one is based on the representation given for the frontal weak Heyting algebras. The second one is based on certain particular classes of WH-spaces.
format Articulo
Articulo
author Celani, Sergio A.
San Martín, Hernán Javier
author_facet Celani, Sergio A.
San Martín, Hernán Javier
author_sort Celani, Sergio A.
title Frontal operators in weak Heyting algebras
title_short Frontal operators in weak Heyting algebras
title_full Frontal operators in weak Heyting algebras
title_fullStr Frontal operators in weak Heyting algebras
title_full_unstemmed Frontal operators in weak Heyting algebras
title_sort frontal operators in weak heyting algebras
publishDate 2012
url http://sedici.unlp.edu.ar/handle/10915/114720
work_keys_str_mv AT celanisergioa frontaloperatorsinweakheytingalgebras
AT sanmartinhernanjavier frontaloperatorsinweakheytingalgebras
bdutipo_str Repositorios
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