Dependent Classes E72

Abstract

Model theory deals with general classes of structures = models, so the class of rings, the class of algebraically closed elds and other such specic classes. Counting of so called complete types over models in the class has an important role in the development of model theory in general and so called stability theory in particular. In particular understanding the stable classes: those with relatively few complete types over structures from the class, has been central in model theory and its applications. Lately, we have a parallel recounting theorem under reasonable restrictions, counting types up to conjugacy. The classes for which we have few complete types up to conjugacy are proved to be so called dependent. This is a strong indication that there is much to be said on the classes whose models in the relevant cases has few complete types over them, so called dependent classes.