Constructing a group-interval in o-minimal structures

Abstract

Let T be a complete o-minimal theory. Roughly said, T has the CF property if every definable family of functions is, locally, a one-dimensional family. We show that if T has the CF property and it is nontrivial then an interval of an ordered abelian group is definable in every model of T. Along the way we develop a general notion of dimension for definable quotients in o-minimal structures.