A counterexample to Petrykowski's conjecture

Abstract

We construct a simple expansion of the theory of nonabelian free groups in which the group admits a global type with bounded left-translation orbit but is not definably amenable. This extends the construction of Chernikov, Hrushovski, Kruckman, Krupi\'nski, Moconja, Pillay, and Ramsey, and gives a counterexample to Petrykowski's conjecture.