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

We introduce the class COUS 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 COUS and EOP are Ramsey classes. In addition, we give an application of our results to calculus of universal minimal flows.

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