Hyperbolic towers and independent generic sets in the theory of free groups

Larsen Louder; Chloé Perin; Rizos Sklinos

doi:10.1215/00294527-2143988

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arXiv · 1208.2858

Hyperbolic towers and independent generic sets in the theory of free groups

Larsen Louder·Chloé Perin·Rizos Sklinos

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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.

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BibTeX RIS

Larsen Louder, Chloé Perin, Rizos Sklinos. 2012-08-14. Hyperbolic towers and independent generic sets in the theory of free groups. https://doi.org/10.1215/00294527-2143988

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