Weakly binary expansions of dense meet-trees

We compute the domination monoid in the theory (Formula presented.) of dense meet-trees. In order to show that this monoid is well-defined, we prove weak binarity of (Formula presented.) and, more generally, of certain expansions of it by binary relations on sets of open cones, a special case being the theory (Formula presented.) from [7]. We then describe the domination monoids of such expansions in terms of those of the expanding relations.