If the countable group has a nonabelian free subgroup, then there exists a standard Borel -space such that the corresponding orbit equivalence relation is countable universal. In this paper, we will consider the question of whether the converse also holds.
Cite this article
Simon Thomas, Universal Borel actions of countable groups. Groups Geom. Dyn. 6 (2012), no. 2, pp. 389–407