Alf Dolich : Uniform finiteness and infinite discrete sets

Posted by Matthias Aschenbrenner , part of the Logic Seminar.

At

Sept. 26, 2006, 4 p.m.

In

SEO 427

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.