London Mathematical Society and EPSRC Short Instructional Course  Model Theory
University of Leeds
1823 July 2010
Organiser: Dugald Macpherson
Lecture Course I Introduction to geometric stability theory (David Evans, UEA) Geometric stability theory grew out of Morley's work on uncountably categorical structures. Originally developed by Shelah as the study of the `classifiability' of the models of a theory, it has been shown to have a much wider mathematical significance, largely through the work of Hrushovski and Zilber. These lectures will look at some of the characteristic aspects of the theory, focusing on the basic notion of a strongly minimal structure : a structure which cannot be split into two infinite definable pieces. Classical examples of these are pure sets, vector spaces (in a suitable language), and algebraically closed fields. All of these carry a natural notion of dimension which is generalized by the modeltheoretic notion of Morley rank . The Trichotomy Conjecture from the 1980's predicted that any strongly minimal structure should resemble one of these examples. Counterexamples to this produced by Hrushovski in 1988 opened the door to unexpected developments in the model theory of the exponential function and analytic structures.
The lectures will cover: basic model theory with examples; strongly minimal structures; Morley rank; amalgamation constructions and Hrushovski's counterexamples to trichotomy.
