Diophanting geometry over groups II: Completions, closures and formal solutions
- Z. Sela
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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.
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- Diophanting geometry over groups II: Completions, closures and formal solutions
Israel Journal of Mathematics
Volume 134, Issue 1 , pp 173-254
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- Z. Sela (1)
- Author Affiliations
- 1. Institute of Mathematics, The Hebrew University of Jerusalem, 91904, Givat Ram, Jerusalem, Israel