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

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