Bulletin of Symbolic Logic 10 (3):334-366 (2004)
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) is categorical in all powers. Zilber's trichotomy conjecture for first order categorical structures was refuted by Hrushovski, by the introducion of a special kind of Abstract Elementary Class. Zilber uses a powerful and essentailly infinitary variant on these techniques to investigate complex exponentiation. This not only demonstrates the relevance of Shelah's model theoretic investigations to mainstream mathematics but produces new results and conjectures in algebraic geometry
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References found in this work BETA
A New Strongly Minimal Set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
Logic with the Quantifier “There Exist Uncountably Many”.H. Jerome Keisler - 1970 - Annals of Mathematical Logic 1 (1):1-93.
Stable Generic Structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.
Classification of Δ-Invariant Amalgamation Classes.Roman D. Aref'ev, John T. Baldwin & Marco Mazzucco - 1999 - Journal of Symbolic Logic 64 (4):1743-1750.
Weight Ω in Stable Theories with Few Types.Bernhard Herwig - 1995 - Journal of Symbolic Logic 60 (2):353-373.
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