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Preprint Number 392

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392. Olga Kharlampovich, Alexei Myasnikov
Definable subsets in a free group

Submission date: 2 November 2011.


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.

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