Weakly binary expansions of dense meet-trees

Abstract

We compute the domination monoid in the theory DMT of dense meettrees. In order to show that this monoid is well-defined, we prove weak binarity of DMT and, more generally, of certain expansions of it by binary relations on sets of open cones, a special case being the theory DTR from [EK19]. We then describe the domination monoids of such expansions in terms of those of the expanding relations.