An Isaac Newton Institute Workshop

An Introduction to Recent Applications of Model Theory

Model theory of algebraically closed valued fields

Authors: H.D. Macpherson (University of Leeds), D.Lippel (University of Notre dame)

Abstract

This tutorial of 5 lectures will be an exposition of a proof of elimination of imaginaries for the theory of algebraically closed valued fields (ACVF), when certain extra sorts from M^eq (coset spaces) are added. The proof will be based on that of [1], though further recent ideas of Hrushovski may be incorporated. The tutorial will begin with a general account of the basic model theory of ACVF and the notion of elimination of imaginaries, and will end with further developments from [2]: in particular, the notion of stable domination.

1. D. Haskell, E. Hrushovski, H.D. Macpherson, `Definable sets in algebraically closed valued fields. Part I: elimination of imaginaries', preprint.

2. D. Haskell E. Hrushovski, H.D. Macpherson, `Definable sets in algebraically closed valued fields. Part II: stable domination and independence.'