Israel Journal of Mathematics

, Volume 134, Issue 1, pp 173–254

Diophanting geometry over groups II: Completions, closures and formal solutions

Article

DOI: 10.1007/BF02787407

Cite this article as:
Sela, Z. Isr. J. Math. (2003) 134: 173. doi:10.1007/BF02787407

Abstract

This paper is the second 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 second paper we generalize Merzlyakov’s theorem on the existence of a formal solution associated with a positive sentence [Me]. We first construct a formal solution to a generalAE sentence which is known to be true over some variety, and then develop tools that enable us to analyze the collection of all such formal solutions.

Copyright information

© The Hebrew University Magnes Press 2003

Authors and Affiliations

  1. 1.Institute of MathematicsThe Hebrew University of JerusalemGivat RamIsrael