Linear O-minimal structures

James Loveys, Ya'acov Peterzil

Research output: Contribution to journalArticlepeer-review


A linearly ordered structure {Mathematical expression} is called o-minimal if every definable subset of M is a finite union of points and intervals. Such an {Mathematical expression} is a CF structure if, roughly said, every definable family of curves is locally a one-parameter family. We prove that if {Mathematical expression} is a CF 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.

Original languageEnglish
Pages (from-to)1-30
Number of pages30
JournalIsrael Journal of Mathematics
Issue number1-2
StatePublished - Feb 1993
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Linear O-minimal structures'. Together they form a unique fingerprint.

Cite this