Submission date: 2 November 2011.

Abstract:

We give a description of definable subsets in a free non-abelian group F that follows from our work on the Tarski problems. As a corollary we show that proper non-abelian subgroups of F are not definable (Malcev's problem) and prove Bestvina and Feighn's result that definable subsets in a free group are either negligible or co-negligible.

Mathematics Subject Classification: 20E05, 03CXX

Keywords and phrases:

Full text arXiv 1111.0577: pdf, ps.