The domination monoid in o-minimal theories

Abstract

We study the monoid of global invariant types modulo dominationequivalence 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 [EHM19], this allows us to compute the domination monoid in the weakly o-minimal theory of Real Closed Valued Fields.