Submission date: 19 August 2015.

Abstract:

We investigate correspondences between extreme amenability and amenability of automorphism groups of Fraïssé-Hrushovski generic structures that are obtained from smooth classes, and their Ramsey type properties of their smooth classes, similar to Kechris, Pestov and Todorcevic, and Tatch Moore. In particular, we focus on some Fraïssé-Hrushovski generic structures that are obtained from pre-dimension functions. Indeed, we prove that automorphism groups of ordered Hrushovski generic graphs are not extremely amenable in both cases of collapsed and uncollapsed. Moreover, we prove that automorphism groups of Fraïssé-Hrushovski generic structures that are obtained from pre-dimension functions with rational coefficients are not amenable.

Mathematics Subject Classification: 03C15, 20B27, 05D10, 43A07

Keywords and phrases:

Full text arXiv 1508.04628: pdf, ps.