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Satisfaction for n-th order languages defined in n-th order languages

Journal of Symbolic Logic 30 (1):13-25 (1965)

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Harmonious logic: Craig’s interpolation theorem and its descendants.Solomon Feferman - 2008 - Synthese 164 (3):341-357.details Though deceptively simple and plausible on the face of it, Craig's interpolation theorem 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 (...) Download Export citation Bookmark 5 citations
Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent?James Owen Weatherall - 2016 - Erkenntnis 81 (5):1073-1091.details I argue that a criterion of theoretical equivalence due to Glymour :227–251, 1977) does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is “yes”, at least on one natural understanding of Newtonian gravitation. Download Export citation Bookmark 74 citations
Harmonious logic: Craig’s interpolation theorem and its descendants.Solomon Feferman - 2008 - Synthese 164 (3):341 - 357.details 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, (...) Download Export citation Bookmark 5 citations
Dependence of variables construed as an atomic formula.Jouko Väänänen & Wilfrid Hodges - 2010 - Annals of Pure and Applied Logic 161 (6):817-828.details We define a logic capable of expressing dependence of a variable on designated variables only. Thus has similar goals to the Henkin quantifiers of [4] and the independence friendly logic of [6] that it much resembles. The logic achieves these goals by realizing the desired dependence declarations of variables on the level of atomic formulas. By [3] and [17], ability to limit dependence relations between variables leads to existential second order expressive power. Our avoids some difficulties arising in the original (...) Download Export citation Bookmark 2 citations
The Craig Interpolation Theorem in abstract model theory.Jouko Väänänen - 2008 - Synthese 164 (3):401-420.details The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics is small. Download Export citation Bookmark 2 citations

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