Kurt Gödel Research Center

2006 seminar talk: Finitary Abstract Elementary Classes

Talk held by Meeri Kesälä (University of Helsinki) at the KGRC seminar on 2006-05-04.

Abstract

We know that first order logic fails to capture many natural classes of structures that appear in mathematics. Several generalizations of model-theoretical tools to non-elementary classes (Shelah 1985) is very general. We do not study structures in any specific language, but give axioms for an abstract elementary substructure-relation. However, if we want to study for example stability theory in this context, we may have to add some more specific assumptions for the class. We introduce finitary abstract elementary classes, a subclass of abstract elementary classes with many good properties. We also compare finitary classes to some other non-elementary classes by studying the behaviour of Galois types and category transfer. This is joint work with Tapani Hyttinen.