Israel Journal of Mathematics

, Volume 150, Issue 1, pp 1–197

Diophantine geometry over groups V1: Quantifier elimination I


DOI: 10.1007/BF02762378

Cite this article as:
Zela, Z. Isr. J. Math. (2005) 150: 1. doi:10.1007/BF02762378


This paper is the first part (out of two) of the fifth paper 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 two papers on quantifier elimination we use the iterative procedure that validates the correctness of anAE sentence defined over a free group, presented in the fourth paper, to show that the Boolean algebra ofAE sets defined over a free group is invariant under projections, and hence show that every elementary set defined over a free group is in the Boolean algebra ofAE sets. The procedures we use for quantifier elimination, presented in this paper and its successor, enable us to answer affirmatively some of Tarski's questions on the elementary theory of a free group in the sixth paper of this sequence.

Copyright information

© Hebrew University 2005

Authors and Affiliations

  • Z. Zela
    • 1
  1. 1.Institute of MathematicsThe Hebrew University of Jerusalem Givat RamJerusalemIsrael