Unstable structures definable in o-minimal theories
Logic
2007-05-23 v1
Abstract
Let M be an o-minimal structure with elimination of imaginaries, N an unstable structure definable in M. Then there exists X, interpretable in N, such that X with all the structure induced from N is o-minimal. In particular X is linearly ordered. As part of the proof we show: Theorem 1: If the M-dimenson of N is 1 then any 1-N-type is either strongly stable or finite by o-minimal. Theorem 2: If N is N-minimal then it is 1-M-dimensional.
Cite
@article{arxiv.0704.3844,
title = {Unstable structures definable in o-minimal theories},
author = {Assaf Hasson and Alf Onshuus},
journal= {arXiv preprint arXiv:0704.3844},
year = {2007}
}