Automorphism groups of generic structures: extreme amenability and amenability

作者：Ghadernezhad Zaniar^*; Khalilian Hamed; Pourmahdian Massoud

来源：Fundamenta Mathematicae, 2018, 242(1): 1-23.

DOI：10.4064/fm435-10-2017

• automorphism groups
• generic structures
• extreme amenable groups
• amenable groups
• structural Ramsey properties
• convex Ramsey property

This paper presents some correspondences between (extreme) amenability of automorphism groups of Fraisse-Hrushovski generic structures, and Ramsey type properties of their smooth classes, similar to results of Kechris, Pestov and Todorcevic (2005) and Moore (2013). In particular, we focus on some Fraisse-Hrushovski generic structures that are obtained from the pre-dimension functions delta(alpha) for alpha >= 1. Using these correspondences, it is shown that the automorphism groups of ordered Hrushovski generic graphs are not extremely amenable in both cases of collapsed and uncollapsed structures. Moreover, when alpha is rational we prove that the automorphism groups of Fraisse-Hrushovski generic structures that are obtained from the pre-dimension functions delta(alpha) are not amenable.

• 出版日期2018