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  1. Notes on quasiminimality and excellence.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (3):334-366.
    This paper ties together much of the model theory of the last 50 years. Shelah's attempts to generalize the Morley theorem beyond first order logic led to the notion of excellence, which is a key to the structure theory of uncountable models. The notion of Abstract Elementary Class arose naturally in attempting to prove the categoricity theorem for L ω 1 ,ω (Q). More recently, Zilber has attempted to identify canonical mathematical structures as those whose theory (in an appropriate logic) (...)
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  • Syntactic characterizations of closure under pullbacks and of locally polypresentable categories.Michel Hébert - 1997 - Annals of Pure and Applied Logic 84 (1):73-95.
    We give syntactic characterizations of1. the theories whose categories of models are closed under the formation of pullbacks, and of2. the locally ω-polypresentable categories.A somewhat typical example is the category of algebraically closed fields. Case is proved by classical model-theoretic methods; it solves a problem raised by H. Volger . The solution of case is in the spirit of the ones for the locally ω-presentable and ω-multipresentable cases found by M. Coste and P.T. Johnstone respectively. The problem was raised in (...)
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