Israel Journal of Mathematics

, Volume 81, Issue 1, pp 1–30

Linear O-minimal structures

  • James Loveys
  • Ya’acov Peterzil
Article

DOI: 10.1007/BF02761295

Cite this article as:
Loveys, J. & Peterzil, Y. Israel J. Math. (1993) 81: 1. doi:10.1007/BF02761295

Abstract

A linearly ordered structure\(\mathcal{M} = (M,< , \cdot \cdot \cdot )\) is called o-minimal if every definable subset ofM is a finite union of points and intervals. Such an\(\mathcal{M}\) is aCF structure if, roughly said, every definable family of curves is locally a one-parameter family. We prove that if\(\mathcal{M}\) is aCF structure which expands an (interval in an) ordered group, then it is elementary equivalent to a reduct of an (interval in an) ordered vector space. Along the way we prove several quantifier-elimination results for expansions and reducts of ordered vector spaces.

Copyright information

© Hebrew University 1993

Authors and Affiliations

  • James Loveys
    • 1
  • Ya’acov Peterzil
    • 1
  1. 1.Department of MathematicsMcGill UniversityMontrealCanada