Title: Characterizing Ordered Abelian Groups in the NIP Hierarchy
Speaker: Alf Dolich (CUNY)
Abstract: The independence property gives a rough dividing line between "wild" and "tame" theories. I will focus on the tame side of the divide, namely those theories without the independence property, generally referred to as the NIP theories. The class of NIP theories can further be divided into a hierarchy of notions, given by dp-rank, of increasing strength and hence increasing tameness. It is of considerable interest to characterize which ordered fields can be found in any of these levels. In attempting to address this problem one is quickly lead to the problem of attempting to characterize which ordered Abelian groups may be found in these various levels of the NIP hierarchy. In this talk I will give a simple algebraic description of the ordered Abelian groups in any level of the hierarchy.
