Definable sets in a hyperbolic group

الأصل · EN

We give a description of definable sets P=(p₁,..., pₘ) in a free non-abelian group F and in a torsion-free non-elementary hyperbolic group G that follows from our work on the Tarski problems. This answers Malcev's question for F. As a corollary we show that proper non-cyclic subgroups of F and G are not definable and prove Bestvina and Feighn's result that definable subsets P=(p) in a free group are either negligible or co-negligible in their terminology.