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.
Finitary Abstract Elementary Classes
04.05.2006 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25