Weakly binary expansions of dense meet-trees

TL;DR

This paper analyzes the domination monoid in the theory of dense meet-trees, proving weak binarity and describing the monoid structure in expanded theories with binary relations.

Contribution

It establishes weak binarity of DMT and related expansions, and characterizes their domination monoids in terms of the expanding relations.

Findings

Domination monoid computed for DMT

Weak binarity of DMT proved

Descriptions of domination monoids in expanded theories

Abstract

We compute the domination monoid in the theory DMT of dense meet-trees. 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 arXiv:1909.04626. We then describe the domination monoids of such expansions in terms of those of the expanding relations.