Submission date: 14 August 2012.

Abstract:

We use hyperbolic towers to answer some model theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the generic type p_0, but that there is a finitely generated model which omits p_0^{(2)}. We exhibit a finitely generated model in which there are two maximal independent sets of realizations of the generic type which have different cardinalities. We also show that a free product of homogeneous groups is not necessarily homogeneous.

Mathematics Subject Classification: 20E05, 20F67, 03C07

Keywords and phrases:

Full text arXiv 1208.2858: pdf, ps.