Notre Dame Journal of Formal Logic

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

Larsen Louder, Chloé Perin, and Rizos Sklinos

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 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.

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1376053777

Digital Object Identifier
doi:10.1215/00294527-2143988

Mathematical Reviews number (MathSciNet)
MR3091669

Zentralblatt MATH identifier
1288.20030

Subjects
Primary: 20F67: Hyperbolic groups and nonpositively curved groups
Secondary: 03C45: Classification theory, stability and related concepts [See also 03C48]

Keywords
free group hyperbolic towers stable groups generic type homogeneity

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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