English

The domination monoid in o-minimal theories

Logic 2025-03-14 v1

Abstract

We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes of 1-types. We show this to hold in Real Closed Fields, where generators of this monoid correspond to invariant convex subrings of the monster model. Combined with arxiv:1702.06504, this allows us to compute the domination monoid in the weakly o-minimal theory of Real Closed Valued Fields.

Keywords

Cite

@article{arxiv.2008.01770,
  title  = {The domination monoid in o-minimal theories},
  author = {Rosario Mennuni},
  journal= {arXiv preprint arXiv:2008.01770},
  year   = {2025}
}

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31 pages