# Ordered structures with dense/co-dense sets

## Alf Dolich

### The City University of New York

The canonical class of densely ordered structures which may be considered “tame” are the o-minimal structures – namely those structures (M,<,...) where any definable subset X is a finite union of points and intervals. In this talk I will consider structure (M,<,...) in which there are definable subsets which are dense and co-dense in the line yet which may still be considered "tame". I will outline some of the general theory of these structures, compare the model theoretic properties of the examples, and discuss various open problems arising out of this study.

Professor Dolich (Ph.D. 2002 University of Maryland, M.A. Columbia University, B.A. University of Pennsylvania) held a VIGRE Van Vleck Assistant Professorship at the University of Wisconsin, Madison, before coming to the New York area, where he now holds an Assistant Professor position at Kingsborough CC of CUNY. Professor Dolich conducts research in model theory, simple theories, and o-minimal theories with secondary interests in algebraic geometry and set theory.