Logic Seminar

A countable group is highly transitive if it admits an embedding in the permutation group of the integers with dense image. I will present a joint work with Pierre Fima, Soyoung Moon and Yves Stalder where we show that a large class of groups acting on trees are highly transitive, which yields a characterization of high transitivity for groups admitting a minimal faithful action of general type on a tree thanks to the work of Le Boudec and Matte Bon. Our proof is new even for the free group on two generators and I will give a detailed overview in this very particular case, showing that the generic transitive action of the free group on two generators is highly transitive.