Submission date: 2 November 2011.

Abstract:

We give a description of definable subsets 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. As a corollary we show that proper non-cyclic subgroups of F and G are not definable (this answers Malcev's question for F) and prove Bestvina and Feighn's result that definable subsets in a free group are either negligible or co-negligible.

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Full text arXiv 1111.0577: pdf, ps.