Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 54, Number 3-4 (2013), 521-539.
Hyperbolic Towers and Independent Generic Sets in the Theory of Free Groups
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 but that there is a finitely generated model which omits . 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.
Notre Dame J. Formal Logic, Volume 54, Number 3-4 (2013), 521-539.
First available in Project Euclid: 9 August 2013
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Louder, Larsen; Perin, Chloé; Sklinos, Rizos. Hyperbolic Towers and Independent Generic Sets in the Theory of Free Groups. Notre Dame J. Formal Logic 54 (2013), no. 3-4, 521--539. doi:10.1215/00294527-2143988. https://projecteuclid.org/euclid.ndjfl/1376053777