Hyperbolic Towers and Independent Generic Sets in the Theory of Free Groups

@article{Louder2013HyperbolicTA,
  title={Hyperbolic Towers and Independent Generic Sets in the Theory of Free Groups},
  author={Larsen Louder and Chlo{\'e} Perin and Rizos Sklinos},
  journal={Notre Dame J. Formal Log.},
  year={2013},
  volume={54},
  pages={521-539}
}
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 p0 but that there is a finitely generated model which omits p(2)0. 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… 

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