Submission date: 30 September 2014.

Abstract:

[22 pages, 2 figures. To appear in the Turkish Journal of Mathematics. Replaces arXiv:1205.4662]

We use pseudo-Anosov homeomorphisms of surfaces in order to prove that the first order theory of non abelian free groups, T_{fg}, is n-ample for any n inω. This result adds to the work of Pillay, that proved that T_{fg} is non CM-trivial. The sequence witnessing ampleness is a sequence of primitive elements in F_ω.
Our result provides an alternative proof to the main result of a preprint by Ould Houcine-Tent. We also add an appendix in which we make a few remarks on Sela's paper on imaginaries in torsion free hyperbolic groups. In particular we give alternative transparent proofs concerning the non-elimination of certain imaginaries.

Mathematics Subject Classification:

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Full text arXiv 1409.8599: pdf, ps.