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

Z. Sela*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


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 general AE 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.

Original languageAmerican English
Pages (from-to)173-254
Number of pages82
JournalIsrael Journal of Mathematics
StatePublished - 2003


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