Ramsey properties of finite posets. II
type: Item
instance of: scholarly article
title: Ramsey properties of finite posets. II
zbMATH Open document ID: 1254.03067
author: Miodrag Sokić
published in: Order
publication date: 2012-03-23T00:00:00Z
review text: 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.
reviewed by: Vera Koponen
Mathematics Subject Classification ID: 03C13
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 03C15
zbMATH DE Number: 6018081
zbMATH Keywords: poset
zbMATH Keywords: Fraïssé class
zbMATH Keywords: minimal flow
zbMATH Keywords: Ramsey property
zbMATH Keywords: extreme amenability
MaRDI profile type: Publication
full work available at URL: s11083-011-9196-2
OpenAlex ID: W1981998844
cites work: Q4331784
cites work: Q4003410
cites work: Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups
cites work: Q4323294
cites work: Partitions of finite relational and set systems
cites work: Ramsey classes of set systems
cites work: Q3415741
cites work: Countable homogeneous partially ordered sets
DOI: 10.1007/S11083-011-9196-2
description: scientific article; zbMATH DE number 6018081