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 language | English |
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Pages (from-to) | 1-30 |
Number of pages | 30 |
Journal | Israel Journal of Mathematics |
Volume | 81 |
Issue number | 1-2 |
DOIs | |
State | Published - Feb 1993 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics