David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 164 (3):341 - 357 (2008)
Though deceptively simple and plausible on the face of it, Craig's interpolation theorem (published 50 years ago) has proved to be a central logical property that has been used to reveal a deep harmony between the syntax and semantics of first order logic. Craig's theorem was generalized soon after by Lyndon, with application to the characterization of first order properties preserved under homomorphism. After retracing the early history, this article is mainly devoted to a survey of subsequent generalizations and applications, especially of many-sorted interpolation theorems. Attention is also paid to methodological considerations, since the Craig theorem and its generalizations were initially obtained by proof-theoretic arguments while most of the applications are model-theoretic in nature. The article concludes with the role of the interpolation property in the quest for "reasonable" logics extending first-order logic within the framework of abstract model theory
|Keywords||Interpolation theorems Preservation theorems Many-sorted languages Extensions of first-order logic Abstract model theory|
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References found in this work BETA
Jon Barwise (1969). Infinitary Logic and Admissible Sets. Journal of Symbolic Logic 34 (2):226-252.
William Craig (1957). Linear Reasoning. A New Form of the Herbrand-Gentzen Theorem. Journal of Symbolic Logic 22 (3):250-268.
William Craig (1965). Satisfaction for N-Th Order Languages Defined in N-Th Order Languages. Journal of Symbolic Logic 30 (1):13-25.
William Craig (1957). Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory. Journal of Symbolic Logic 22 (3):269-285.
Citations of this work BETA
H. Jerome Keisler & Jeffrey M. Keisler (2012). Craig Interpolation for Networks of Sentences. Annals of Pure and Applied Logic 163 (9):1322-1344.
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