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

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-...

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Detalles Bibliográficos
Autores principales:	Castiglioni, José Luis, San Martín, Hernán Javier
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2012
Materias:	Matemática Amalgamation property Craig’s interpolation theorem Heyting algebras with operators Extensions of intuitionistic propositional calculus
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/146211
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-146211
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Matemática Amalgamation property Craig’s interpolation theorem Heyting algebras with operators Extensions of intuitionistic propositional calculus
spellingShingle	Matemática Amalgamation property Craig’s interpolation theorem Heyting algebras with operators Extensions of intuitionistic propositional calculus Castiglioni, José Luis San Martín, Hernán Javier On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
topic_facet	Matemática Amalgamation property Craig’s interpolation theorem Heyting algebras with operators Extensions of intuitionistic propositional calculus
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.
format	Articulo Articulo
author	Castiglioni, José Luis San Martín, Hernán Javier
author_facet	Castiglioni, José Luis San Martín, Hernán Javier
author_sort	Castiglioni, José Luis
title	On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
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
publishDate	2012
url	http://sedici.unlp.edu.ar/handle/10915/146211
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On some Classes of Heyting Algebras with Successor that have the Amalgamation Property

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