Title: Sentences over Random Groups

Abstract: The Tarski question states that the f.g. non-abelian free groups share the same first order theory. In 2006, Z. Sela answered it affirmatively. Hence, a natural question is to seek for groups that can or cannot be distinguished from the non-abelian free groups by a given first order sentence. We prove that almost all the (f.g.) groups are not so. Namely, we prove that a random group (in the Gromov density model, for any density d<.5), cannot be distinguished from the f.g. non-abelian free groups by a given (minimal rank) sentence, in overwhelming probability.

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