Constructing a group-interval in o-minimal structures

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)85-100
Number of pages16
JournalJournal of Pure and Applied Algebra
Issue number1
StatePublished - 3 Jun 1994
Externally publishedYes

Bibliographical note

Funding 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


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