September 2004 Notes on quasiminimality and excellence
John T. Baldwin
Bull. Symbolic Logic 10(3): 334-366 (September 2004). DOI: 10.2178/bsl/1102022661


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 Lω1(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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John T. Baldwin. "Notes on quasiminimality and excellence." Bull. Symbolic Logic 10 (3) 334 - 366, September 2004.


Published: September 2004
First available in Project Euclid: 2 December 2004

zbMATH: 1064.03023
MathSciNet: MR2083288
Digital Object Identifier: 10.2178/bsl/1102022661

Rights: Copyright © 2004 Association for Symbolic Logic


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Vol.10 • No. 3 • September 2004
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