Ramsey property, ultrametric spaces, finite posets, and universal minimal flows

摘要

We introduce the class COU_S of finite ultrametric spaces with distances in the set S and with two additional linear orderings. We also introduce the class EOP of finite posets with two additional linear orderings. In this paper, we prove that COU_S and EOP are Ramsey classes. In addition, we give an application of our results to calculus of universal minimal flows.