Israel Journal of Mathematics

, Volume 134, Issue 1, pp 173–254 | Cite as

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



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.


Limit Group Free Abelian Group Dehn Twist Vertex Group Truth Sentence 
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Copyright information

© The Hebrew University Magnes Press 2003

Authors and Affiliations

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

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