The free group does not have the finite cover property
Logic
2017-06-08 v2 Group Theory
Geometric Topology
Abstract
We prove that the first order theory of nonabelian free groups eliminates the "there exists infinitely many" quantifier (in eq). Equivalently, since the theory of nonabelian free groups is stable, it does not have the finite cover property. We also extend our results to torsion-free hyperbolic groups under some conditions.
Keywords
Cite
@article{arxiv.1312.0586,
title = {The free group does not have the finite cover property},
author = {Rizos Sklinos},
journal= {arXiv preprint arXiv:1312.0586},
year = {2017}
}
Comments
23 pages, to appear in the Israel J. Math