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  1. The Craig Interpolation Theorem in abstract model theory.Jouko Väänänen - 2008 - Synthese 164 (3):401-420.
    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.
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  • On κ-like structures which embed stationary and closed unbounded subsets.James H. Schmerl - 1976 - Annals of Mathematical Logic 10 (3-4):289-314.
  • δ-Logics and generalized quantifiers.J. A. Makowsky - 1976 - Annals of Mathematical Logic 10 (2):155-192.
  • Countably decomposable admissible sets.Menachem Magidor, Saharon Shelah & Jonathan Stavi - 1984 - Annals of Pure and Applied Logic 26 (3):287-361.
    The known results about Σ 1 -completeness, Σ 1 -compactness, ordinal omitting etc. are given a unified treatment, which yields many new examples. It is shown that the unifying theorem is best possible in several ways, assuming V = L.
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  • Axioms for abstract model theory.K. Jon Barwise - 1974 - Annals of Mathematical Logic 7 (2-3):221-265.
  • Absolute logics and L∞ω.K. Jon Barwise - 1972 - Annals of Mathematical Logic 4 (3):309-340.
  • Axioms for abstract model theory.K. J. Barwise - 1974 - Annals of Mathematical Logic 7 (2-3):221-265.
  • Infinitary propositional relevant languages with absurdity.Guillermo Badia - 2017 - Review of Symbolic Logic 10 (4):663-681.
    Analogues of Scott's isomorphism theorem, Karp's theorem as well as results on lack of compactness and strong completeness are established for infinitary propositional relevant logics. An "interpolation theorem" for the infinitary quantificational boolean logic L-infinity omega. holds. This yields a preservation result characterizing the expressive power of infinitary relevant languages with absurdity using the model-theoretic relation of relevant directed bisimulation as well as a Beth definability property.
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