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  1. Super/rosy L k -theories and classes of finite structures.Cameron Donnay Hill - 2013 - Annals of Pure and Applied Logic 164 (10):907-927.
    We recover the essentials of þ-forking, rosiness and super-rosiness for certain amalgamation classes K, and thence of finite-variable theories of finite structures. This provides a foundation for a model-theoretic analysis of a natural extension of the “LkLk-Canonization Problem” – the possibility of efficiently recovering finite models of T given a finite presentation of an LkLk-theory T. Some of this work is accomplished through different sorts of “transfer” theorem to the first-order theory TlimTlim of the direct limit. Our results include, to (...)
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  • Some aspects of model theory and finite structures.Eric Rosen - 2002 - Bulletin of Symbolic Logic 8 (3):380-403.
    Model theory is concerned mainly, although not exclusively, with infinite structures. In recent years, finite structures have risen to greater prominence, both within the context of mainstream model theory, e.g., in work of Lachlan, Cherlin, Hrushovski, and others, and with the advent of finite model theory, which incorporates elements of classical model theory, combinatorics, and complexity theory. The purpose of this survey is to provide an overview of what might be called the model theory of finite structures. Some topics in (...)
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  • Upward Categoricity from a Successor Cardinal for Tame Abstract Classes with Amalgamation.Olivier Lessmann - 2005 - Journal of Symbolic Logic 70 (2):639 - 660.
    This paper is devoted to the proof of the following upward categoricity theorem: Let K be a tame abstract elementary class with amalgamation, arbitrarily large models, and countable Löwenheim-Skolem number. If K is categorical in ‮א‬₁ then K is categorical in every uncountable cardinal. More generally, we prove that if K is categorical in a successor cardinal λ⁺ then K is categorical everywhere above λ⁺.
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  • Upward categoricity of very tame abstract elementary classes with amalgamation.John T. Baldwin & Olivier Lessmann - 2006 - Annals of Pure and Applied Logic 143 (1-3):29-42.
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  • Uncountable categoricity of local abstract elementary classes with amalgamation.John T. Baldwin & Olivier Lessmann - 2006 - Annals of Pure and Applied Logic 143 (1-3):29-42.
    We give a complete and elementary proof of the following upward categoricity theorem: let be a local abstract elementary class with amalgamation and joint embedding, arbitrarily large models, and countable Löwenheim–Skolem number. If is categorical in 1 then is categorical in every uncountable cardinal. In particular, this provides a new proof of the upward part of Morley’s theorem in first order logic without any use of prime models or heavy stability theoretic machinery.
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  • Finite and Infinite Model Theory-A Historical Perspective.John Baldwin - 2000 - Logic Journal of the IGPL 8 (5):605-628.
    We describe the progress of model theory in the last half century from the standpoint of how finite model theory might develop.
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  • Upward categoricity from a successor cardinal for tame abstract classes with amalgamation.Olivier Lessmann - 2005 - Journal of Symbolic Logic 70 (2):639-660.
    This paper is devoted to the proof of the following upward categoricity theorem: Let.
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