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arXiv · 2008.01770

The domination monoid in o-minimal theories

Rosario Mennuni
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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.

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Rosario Mennuni. 2020-08-04. The domination monoid in o-minimal theories. https://doi.org/10.1142/s0219061321500306

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