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Hyperbolic towers and independent generic sets in the theory of free groups
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Louder, Larsen, Perin, Chloé and Sklinos, Rizos (2013) Hyperbolic towers and independent generic sets in the theory of free groups. Notre Dame Journal of Formal Logic, Volume 54 (Number 3-4). pp. 521-539. doi:10.1215/00294527-2143988 ISSN 0029-4527.
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Official URL: http://dx.doi.org/10.1215/00294527-2143988
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 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.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Notre Dame Journal of Formal Logic | ||||
Publisher: | Duke University Press | ||||
ISSN: | 0029-4527 | ||||
Official Date: | 9 August 2013 | ||||
Dates: |
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Volume: | Volume 54 | ||||
Number: | Number 3-4 | ||||
Page Range: | pp. 521-539 | ||||
DOI: | 10.1215/00294527-2143988 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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