Abstract
This paper introduces the notion of syntactic feature to provide a unified treatment of earlier model theoretic proofs of both the compactness and interpolation theorems for a variety of two valued logics including sentential logic, first order logic, and a family of modal sentential logic includingM,B,S 4 andS 5. The compactness papers focused on providing a proof of the consequence formulation which exhibited the appropriate finite subset. A unified presentation of these proofs is given by isolating their essential feature and presenting it as an abstract principle about syntactic features. The interpolation papers focused on exhibiting the interpolant. A unified presentation of these proofs is given by isolating their essential feature and presenting it as a second abstract principle about syntactic features. This second principle reduces the problem of exhibiting the interpolant to that of establishing the existence of a family of syntactic features satisfying certain conditions. The existence of such features is established for a variety of logics (including those mentioned above) by purely combinatorial arguments.
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Weaver, G.E. Syntactic features and synonymy relations: a unified treatment of some proofs of the compactness and interpolation theorems. Stud Logica 53, 325–342 (1994). https://doi.org/10.1007/BF01054715
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DOI: https://doi.org/10.1007/BF01054715