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

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Matemática, Facultad de Cs. Exactas, Universidad Nacional de La Plata, CC 172, La Plata, 1900, Argentina

    José L. Castiglioni & Hernán J. San Martín

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  1. José L. Castiglioni
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  2. Hernán J. San Martín
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Correspondence to José L. Castiglioni.

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Castiglioni, J.L., San Martín, H.J. On some Classes of Heyting Algebras with Successor that have the Amalgamation Property. Stud Logica 100, 1255–1269 (2012). https://doi.org/10.1007/s11225-012-9451-6

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  • DOI: https://doi.org/10.1007/s11225-012-9451-6

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