Hyperbolic towers and independent generic sets in the theory of free groups

Larsen Louder, Chloé Perin, Rizos Sklinos

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageAmerican English
Pages (from-to)521-539
Number of pages19
JournalNotre Dame Journal of Formal Logic
Volume54
Issue number3-4
DOIs
StatePublished - 2013
Externally publishedYes

Keywords

  • Free group
  • Generic type
  • Homogeneity
  • Hyperbolic towers
  • Stable groups

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