Syntactic features and synonymy relations: A unified treatment of some proofs of the compactness and interpolation theorems
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Studia Logica 53 (2):325 - 342 (1994)
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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References found in this work BETA
George Weaver (1982). A Note on the Interpolation Theorem in First Order Logic. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (14-18):215-218.
George Weaver (1978). Compactness Theorems for Finitely-Many-Valued Sentenial Logics. Studia Logica 37 (4):413 - 416.
George Weaver & Jeffrey Welaish (1986). Back and Forth Constructions in Modal Logic: An Interpolation Theorem for a Family of Modal Logics. Journal of Symbolic Logic 51 (4):969-980.
C. C. Chang & H. J. Keisler (1976). Model Theory. Journal of Symbolic Logic 41 (3):697-699.
G. Weaver (1978). Compactness theorems for finitely-many-valued logics. Studia Logica 37:413.
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