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
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 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.
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