, Volume 16, Issue 3, pp 707-730
Date: 29 Jun 2006

Diophantine geometry over groups VI: the elementary theory of a free group

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This paper is the sixth in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the sixth paper we use the quantifier elimination procedure presented in the two parts of the fifth paper in the sequence, to answer some of A. Tarski’s problems on the elementary theory of a free group, and to classify finitely generated (f.g.) groups that are elementarily equivalent to a non-abelian f.g. free group.