arXiv:1312.0586 Abstract | arXiv Analytics

arXiv:1312.0586 [math.LO]Abstract References Reviews Resources

The free group does not have the finite cover property

Published 2013-12-02, updated 2017-06-07Version 2

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.

Comments: 23 pages, to appear in the Israel J. Math

Categories: math.LO, math.GR, math.GT

Keywords: finite cover property, torsion-free hyperbolic groups, non abelian free groups eliminates, first order theory

Related articles: Most relevant | Search more

arXiv:0706.3021 [math.LO] (Published 2007-06-20, updated 2007-11-23)

Independence property and hyperbolic groups

Eric Jaligot, Alexey Muranov, Azadeh Neman

arXiv:math/0401307 [math.LO] (Published 2004-01-22, updated 2004-03-31)

Succinct Definitions in the First Order Theory of Graphs

Oleg Pikhurko, Joel Spencer, Oleg Verbitsky

arXiv:1705.04564 [math.LO] (Published 2017-05-07)

First Order Theories of Some Lattices of Open Sets