Algorithmic randomness and Ramsey properties of countable homogeneous structures

Abstract

We study, in the context of algorithmic randomness, the closed amenable subgroups of the symmetric group $S_{\infty }$ of a countable set. In this paper we address this problem by investigating a link between the symmetries associated with Ramsey Fraïssé order classes and algorithmic randomness.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1205.0386