Recent work of Malliaris and Shelah has given a characterization of simple theories in terms of saturation of ultrapowers. The proof involves developing a framework for classifying the complexity of amalgamation patterns in simple theories. The talk will be about the model-theoretic picture of complexity emerging from this analysis.
A model-theorist's view of algebraically closed valued fields
Deirdre Haskell (McMaster University)
MSRI: Simons Auditorium
I will start with the definition of an algebraically closed valued field, and observe the role played by the families of open and closed balls, and how the residue field and value group can be seen in different subfamilies. We will look at the definable sets and definable equivalence classes in one variable, and discuss how to generalise to more variables. This will lead to looking at examples of stably dominated types, which play a fundamental role in the model-theoretic approach to Berkovich space