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Aspects of Geometric Model Theory

In this paper (based on my tutorial in Utrecht) I want to discuss some themes from contemporary model theory, mainly originating in stability theory and classification theory, and point out some mathematical implications. Model theory has become largely the study of definable sets (or the category of definable sets and functions) in given structures, as well as the study of interpretability and bi-interpretability. These can either be specific, such as the field of p-adic numbers (as in applications), or can be arbitrary structures which satisy some model-theoretic hypotheses (stability, ω1-categoricity, ominimality). Among the themes or topics I will touch on are: dimension theory, how a structure is built up from “irreducible bits” (geometries), the fine structure of these “irreducible bits”, modularity, orthogonality, equivariant model theory (definable groups and group actions), quotients and Galois theory. This paper is aimed at the non model-theorist logician. I want to explain a little of what is going on in model theory, but at the same time I do not want to simply repeat what has already been said in numerous surveys of this kind. ∗Supported by an NSF grant