Submission date: 2 December 2013

Abstract:

We prove that the first order theory of non abelian free groups eliminates the “there exists infinitely many” quantifier (in eq). Equivalently, since the theory of non abelian 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.

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Full text arXiv 1312.0586: pdf, ps.