The free group does not have the finite cover property
classification
🧮 math.LO
math.GRmath.GT
keywords
freegroupscoverfinitenonabelianpropertytheoryconditions
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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.
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