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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.
Partially supported by an Israel Academy of Sciences Fellowship.
 M. Bestvina,Rtrees in topology, geometry and group theory, preprint.
 Bestvina, M., Feighn, M. (1995) Stable actions of groups on real trees. Inventiones Mathematicae 121: pp. 287321 CrossRef
 Kharlampovich, O., Myasnikov, A. (2001) Implicit function theorem over free groups and genus problem. Proceedings of the Birmanfest, AMS/IP Studies in Advanced Mathematics 24: pp. 7783
 Merzlyakov, Yu. I. (1966) Positive formulae on free groups. Algebra i Logika 5: pp. 257266
 F. Paulin,Outer automorphisms of hyperbolic groups and small actions on Rtrees, inArboreal Group Theory (R. C. Alperin, ed.), MSRI Publications No. 19, 1991, pp. 331–343.
 Rips, E., Sela, Z. (1994) Structure and rigidity in hyperbolic groups I. Geometric and Functional Analysis 4: pp. 337371 CrossRef
 Rips, E., Sela, Z. (1997) Cyclic splittings of finitely presented groups and the canonical JSJ decomposition. Annals of Mathematics 146: pp. 53104 CrossRef
 Sela, Z. (2001) Diophantine geometry over groups I: MakaninRazborov diagrams. Publications Mathematiques de l’IHES 93: pp. 31105 CrossRef
 Title
 Diophanting geometry over groups II: Completions, closures and formal solutions
 Journal

Israel Journal of Mathematics
Volume 134, Issue 1 , pp 173254
 Cover Date
 20031201
 DOI
 10.1007/BF02787407
 Print ISSN
 00212172
 Online ISSN
 15658511
 Publisher
 SpringerVerlag
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 Authors

 Z. Sela ^{(1)}
 Author Affiliations

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