## Notre Dame Journal of Formal Logic

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

#### 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 $p^{(2)}_{0}$. 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 necessarily homogeneous.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 54, Number 3-4 (2013), 521-539.

Dates
First available in Project Euclid: 9 August 2013

https://projecteuclid.org/euclid.ndjfl/1376053777

Digital Object Identifier
doi:10.1215/00294527-2143988

Mathematical Reviews number (MathSciNet)
MR3091669

Zentralblatt MATH identifier
1288.20030

#### Citation

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

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