Advertisement

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.

Keywords

Boundary Component Limit Group Minimal Rank Vertex Group Quantifier Elimination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Me] Yu. I. Merzlyakov,Positive formulae on free groups, Algebra i Logika5 (1966), 257–266.Google Scholar
  2. [Sc] P. Scott,Subgroups of surface groups are almost geometric, Journal of the London Mathematical Society17 (1978), 555–565.zbMATHCrossRefGoogle Scholar
  3. [Se1] Z. Sela,Diophantine geometry over groups I: Makanin-Razborov diagrams, Publication Mathématiques de l'IHES93 (2001), 31–105.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [Se2] Z. Sela,Diophantine geometry over groups II: Completions, closures and formal solutions, Israel Journal of Mathematics134 (2003), 173–254.zbMATHCrossRefMathSciNetGoogle 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

Personalised recommendations