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

被引：3

作者：

Castiglioni, J. L. ^{[1
]}

San Martin, H. J. ^{[1
]}

机构：

[1] Univ Nacl La Plata, Dept Matemat, Fac Cs Exactas, RA-1900 La Plata, Argentina

来源：

STUDIA LOGICA | 2012年 / 100卷 / 06期

关键词：

Amalgamation property; Craig's interpolation theorem; Heyting algebras with operators; Extensions of intuitionistic propositional calculus;

D O I：

10.1007/s11225-012-9451-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1255 / 1269

页数：15

共 50 条

[1] On some Classes of Heyting Algebras with Successor that have the Amalgamation Property
José L. Castiglioni
Hernán J. San Martín
Studia Logica, 2012, 100 : 1255 - 1269
[2] THE FINITE MODEL PROPERTY FOR THE VARIETY OF HEYTING ALGEBRAS WITH SUCCESSOR
Castiglioni, J. L.
San Martin, H. J.
REVISTA DE LA UNION MATEMATICA ARGENTINA, 2012, 53 (02): : 91 - 96
[3] Classes of algebras without the amalgamation property
Ahmed, Tarek Sayed
LOGIC JOURNAL OF THE IGPL, 2011, 19 (01) : 87 - 104
[4] AMALGAMATION AND INTERPOLATION IN THE CATEGORY OF HEYTING ALGEBRAS
PITTS, AM
JOURNAL OF PURE AND APPLIED ALGEBRA, 1983, 29 (02) : 155 - 165
[5] REPRESENTABILITY AND AMALGAMATION FOR HEYTING POLYADIC ALGEBRAS
Ahmed, Tarek Sayed
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2011, 48 (04) : 509 - 539
[6] DUALITIES FOR EQUATIONAL CLASSES OF BROUWERIAN ALGEBRAS AND HEYTING ALGEBRAS
DAVEY, BA
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 221 (01) : 119 - 146
[7] ON THE VARIETY OF HEYTING ALGEBRAS WITH SUCCESSOR GENERATED BY ALL FINITE CHAINS
Castiglioni, Jose L.
San Martin, Hernan J.
REPORTS ON MATHEMATICAL LOGIC, 2010, 45 : 225 - 248
[8] The variety of quasi-Stone algebras does not have the amalgamation property
Sara-Kaja Fischer
Algebra universalis, 2011, 66
[9] NONDISTRIBUTIVE EQUATIONAL CLASSES OF MODULAR LATTICES FAIL TO HAVE AMALGAMATION PROPERTY
GRATZER, GA
LAKSER, H
JONSSON, B
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 18 (04): : 635 - &
[10] The variety of quasi-Stone algebras does not have the amalgamation property
Fischer, Sara-Kaja
ALGEBRA UNIVERSALIS, 2011, 66 (1-2) : 1 - 3

← 1 2 3 4 5 →