CONSTRUCTING A GROUP-INTERVAL IN O-MINIMAL STRUCTURES

Let T be a complete o-minimal theory. Roughly said, T has the CF prope rty if every definable family of functions is, locally, a one-dimensio nal 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 mo del of T. Along the way we develop a general notion of dimension for d efinable quotients in o-minimal structures.