English

O-minimal residue fields of o-minimal fields

Logic 2010-01-12 v1

Abstract

Let R be an o-minimal field with a proper convex subring V. We axiomatize the class of all structures (R,V) such that k_ind, the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in previous work it was shown that certain first order conditions on (R,V) are sufficient for the o-minimality of k_ind. Here we prove that these conditions are also necessary.

Keywords

Cite

@article{arxiv.1001.1575,
  title  = {O-minimal residue fields of o-minimal fields},
  author = {Jana Maříková},
  journal= {arXiv preprint arXiv:1001.1575},
  year   = {2010}
}