Geometric & Functional Analysis GAFA

, Volume 16, Issue 3, pp 707–730

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

Original Paper

DOI: 10.1007/s00039-006-0565-8

Cite this article as:
Sela, Z. GAFA, Geom. funct. anal. (2006) 16: 707. doi:10.1007/s00039-006-0565-8


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.

Keywords and phrases.

First order theory Tarski problem quantifier elimination elementary equivalence limit groups ω-residually free towers 

AMS Mathematics Subject Classification.

20F65 03B35 20E05 20F10 

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Institute of MathematicsHebrew UniversityJerusalemIsrael

Personalised recommendations