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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| Formato: | Articulo |
| Lenguaje: | Inglés |
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2012
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/146211 |
| Aporte de: | Aportado por :
SEDICI (UNLP) de
Universidad Nacional de La Plata .
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I19-R120-10915-1462112022-11-24T04:07:25Z http://sedici.unlp.edu.ar/handle/10915/146211 issn:0039-3215 issn:1572-8730 On some Classes of Heyting Algebras with Successor that have the Amalgamation Property Castiglioni, José Luis San Martín, Hernán Javier 2012-10-20 2022-11-23T12:16:14Z en Matemática Amalgamation property Craig’s interpolation theorem Heyting algebras with operators Extensions of intuitionistic propositional calculus 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 Articulo Articulo http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf 1255-1269 |
| 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 |
| work_keys_str_mv |
AT castiglionijoseluis onsomeclassesofheytingalgebraswithsuccessorthathavetheamalgamationproperty AT sanmartinhernanjavier onsomeclassesofheytingalgebraswithsuccessorthathavetheamalgamationproperty |
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