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

Z. Sela*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

120 Scopus citations


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.

Original languageAmerican English
Pages (from-to)707-730
Number of pages24
JournalGeometric and Functional Analysis
Issue number3
StatePublished - Jun 2006

Bibliographical note

Funding Information:
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) Partially supported by an Israel Academy of Sciences fellowship.


  • Elementary equivalence
  • First order theory
  • Limit groups
  • Quantifier elimination
  • Tarski problem
  • ω-residually free towers


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