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.
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Partially supported by an Israel Academy of Sciences Fellowship.
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Sela, Z. Diophanting geometry over groups II: Completions, closures and formal solutions. Isr. J. Math. 134, 173–254 (2003). https://doi.org/10.1007/BF02787407
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DOI: https://doi.org/10.1007/BF02787407