Israel Journal of Mathematics

, Volume 143, Issue 1, pp 1–130 | Cite as

Diophantine geometry over groups IV: An iterative procedure for validation of a sentence

Article

Abstract

This paper is the fourth in a series 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 fourth paper we present an iterative procedure that validates the correctness of anAE sentence defined over a free group. The terminating procedure presented in this paper is the basis for our analysis of elementary sets defined over a free group presented in the next papers in the series.

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References

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  3. [Se1] Z. Sela,Diophantine geometry over groups I: Makanin-Razborov diagrams, Publication Mathématiques de l'IHES93 (2001), 31–105.MATHCrossRefMathSciNetGoogle Scholar
  4. [Se2] Z. Sela,Diophantine geometry over groups II: Completions, closures and formal solutions, Israel Journal of Mathematics134 (2003), 173–254.MATHCrossRefMathSciNetGoogle Scholar
  5. [Se3] Z. Sela,Diophantine geometry over groups III: Rigid and solid solutions, Israel Journal of Mathematics, to appear.Google Scholar

Copyright information

© Hebrew University 2004

Authors and Affiliations

  • Z. Sela
    • 1
  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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