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

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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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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, 91904, Givat Ram, Jerusalem, Israel

    Z. Sela

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  1. Z. Sela
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Correspondence to Z. Sela.

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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

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