Archive for Mathematical Logic 45 (8):913-930 (2006)

We study Basic algebra, the algebraic structure associated with basic propositional calculus, and some of its natural extensions. Among other things, we prove the amalgamation property for the class of Basic algebras, faithful Basic algebras and linear faithful Basic algebras. We also show that a faithful theory has the interpolation property if and only if its correspondence class of algebras has the amalgamation property
Keywords Amalgamation  Basic algebra  Basic propositional logic  Heyting algebra  Faithful  Interpolation
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DOI 10.1007/s00153-006-0018-y
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Bounded Distributive Lattices with Strict Implication.Sergio Celani & Ramon Jansana - 2005 - Mathematical Logic Quarterly 51 (3):219-246.
Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
Speaking About Transitive Frames in Propositional Languages.Yasuhito Suzuki, Frank Wolter & Michael Zakharyaschev - 1998 - Journal of Logic, Language and Information 7 (3):317-339.

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