The free group does not have the finite cover property

DOI10.1007/S11856-018-1748-3arXiv1312.0586WikidataQ129441653 ScholiaQ129441653MaRDI QIDQ6246947

Publication date: 2 December 2013

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.

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Geometric group theory (20F65) Free nonabelian groups (20E05) Classification theory, stability, and related concepts in model theory (03C45) Groups acting on trees (20E08) Quantifier elimination, model completeness, and related topics (03C10)

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