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.
Bibliographical noteFunding Information:
* This paper was written with the support of NSERC. The author thanks J. Loveys for his assistance. Current address: Department of Mathematics, Haifa University, Haifa, Israel.
ASJC Scopus subject areas
- Algebra and Number Theory