Logic Seminar
Alf Dolich
UIC
Uniform finiteness and infinite discrete sets
Abstract: Recall that a theory T is said to satisfy uniform finiteness if for any uniformly definable family
of sets there is a natural number N so that any finite set in the family has cardinality at most N.
Let T be an expansion of the theory of dense linear orderings. If T does not satisfy uniform finiteness
then in some model of T there is an infinite definable discrete set. We consider consequences of this fact
and investigate when the converse holds and examples where it does not.
Tuesday September 26, 2006 at 4:00 PM in SEO 427