Independence for types in algebraically closed valued fields

Abstract

Introduction: the historical context. My goal in this article, as it was in the lecture at the Logic Colloquium in Athens, is to survey the notion of independence of types, a fundamental tool in the area of stability theory, and see different ways in which it can be realized in a particular example of an unstable theory, the theory of algebraically closed valued fields. I thank the anonymous referee for many comments which have significantly improved this article. Of course, all remaining errors are my own.