Ramsey properties of finite posets. II
This article continues the classification, initiated in Part I [the author, ibid. 29, No. 1, 1--30 (2012; Zbl 1254.03066)], of classes of finite partial orders which are derived from the Schmerl list of countable ultrahomogeneous partial orders. For more background information see the (longer) review of [loc. cit.]. New Fraïssé classes of partial orders are classified according to whether they have the Ramsey property, or not, and according to whether they have the order property, or not. For this, a `product Ramsey theorem' is proved. The information about the Ramsey property and order property together with techniques of \textit{A. Kechris, V. Pestov} and \textit{S. Todorcevic} [Geom. Funct. Anal. 15, No. 1, 106--189 (2005; Zbl 1084.54014)] are used to get results about extreme amenability and the existence of a universal minimal flow of the automorphism group of the Fraïssé limit of a given class of finite partial orders. This gives new examples of extremely amenable groups and universal minimal flows. In two cases the technique of Kechris et al. is not applicable and a direct calculation of the universal minimal flow is used instead.
scientific article; zbMATH DE number 6018081