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2013 Hyperbolic Towers and Independent Generic Sets in the Theory of Free Groups
Larsen Louder, Chloé Perin, Rizos Sklinos
Notre Dame J. Formal Logic 54(3-4): 521-539 (2013). DOI: 10.1215/00294527-2143988


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 p0(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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Larsen Louder. Chloé Perin. Rizos Sklinos. "Hyperbolic Towers and Independent Generic Sets in the Theory of Free Groups." Notre Dame J. Formal Logic 54 (3-4) 521 - 539, 2013.


Published: 2013
First available in Project Euclid: 9 August 2013

zbMATH: 1288.20030
MathSciNet: MR3091669
Digital Object Identifier: 10.1215/00294527-2143988

Primary: 20F67
Secondary: 03C45

Keywords: free group , generic type , homogeneity , hyperbolic towers , stable groups

Rights: Copyright © 2013 University of Notre Dame


Vol.54 • No. 3-4 • 2013
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