Christine Eagles, Department of Pure Mathematics, University of Waterloo
"Domination in stable theories"
An ongoing project in geometric stability is to interpret model-theoretic notions in a geometric setting. In stable theories we have a notion of independence on sets. For example, in algebraically closed fields independence captures algebraic disjointness. Domination is a model theoretic concept which says when one type captures all the independence relations of another type. In this talk we introduce domination in the context of algebraically closed fields in characteristic zero and then look at domination in differentially closed fields in characteristic zero. We will see a clear characteristic of domination in algebraically closed fields and produce a counter example to this characterization in differentially closed fields.