Linear O-minimal structures

James Loveys, Ya'acov Peterzil

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume81
Issue number1-2
DOIs
StatePublished - Feb 1993
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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