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Israel Journal of Mathematics

, Volume 81, Issue 1–2, pp 1–30 | Cite as

Linear O-minimal structures

  • James Loveys
  • Ya’acov Peterzil
Article

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.

Keywords

Division Ring Finite Union Elementary Extension Quantifier Elimination Order Vector Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1993

Authors and Affiliations

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

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