Sentential logics and Maehara interpolation property

Studia Logica 44 (3):265 - 283 (1985)
With each sentential logic C, identified with a structural consequence operation in a sentential language, the class Matr * (C) of factorial matrices which validate C is associated. The paper, which is a continuation of [2], concerns the connection between the purely syntactic property imposed on C, referred to as Maehara Interpolation Property (MIP), and three diagrammatic properties of the class Matr* (C): the Amalgamation Property (AP), the (deductive) Filter Extension Property (FEP) and Injections Transferable (IT). The main theorem of the paper (Theorem 2.2) is analogous to the Wroski's result for equational classes of algebras [13]. It reads that for a large class of logics the conjunction of (AP) and (FEP) is equivalent to (IT) and that the latter property is equivalent to (MIP).
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DOI 10.1007/BF00394446
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Gaisi Takeuti (1987). Proof Theory. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..

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