Advanced Logic Class

The class of fields with a given absolute Galois group is in general not an elementary class. Looking instead at abstract elementary classes we can show that this class, as well as the class of pairs (F,K), where F is a function field in one variable over a perfect base field K with a fixed absolute Galois group, is abstract elementary. The aim is to show categoricity for the latter class. In this talk, we will be discussing some consequences of basic properties of these two classes.