November 3
Alfred Dolich,
CUNY
Definable sets in rank two expansions of ordered groups
I will discuss work on burden 2 or dp-rank 2 expansions of theories of densely ordered Abelian groups. Such theories allow for some variety in the topological properties of definable subsets in their models and I'll discuss how diverse the collection of definable subsets in a model may be. For example, is it possible to simultaneously define an infinite discrete set and a dense co-dense subset? Answer to such questions often hinge on whether one is working in the inp-rank or dp-rank case (i.e. whether one assumes NIP or not). I will provide definitions in the talk of all the relevant notions. This is joint work with John Goodrick.