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

By Z. Sela. 2003

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Hall’s Theorem for Limit Groups (2006, background): “In [20, 21, 23, 22, 24, 26, 25], Zlil Sela solved a famous problem of Alfred Tarski by classifying the elementarily free groups, those limit groups with the same elementary theory as a free group.”
Limit groups for relatively hyperbolic groups. I. The basic tools (2004, background): “In his remarkable series of papers [38, 39 , 41], Z. Sela has classified those finitely generated groups with the same elementary theory as the free group of rank 2 (see also [40] for a summary).”
Subgroups of direct products of limit groups (2007, background): “The reader unfamiliar with this fascinating class of groups should consult the introductions in [1, 6], the original papers of Sela [22, 23, 24], or those of Kharlampovich and Myasnikov [18, 19, 20] where the subject is approached from a perspective more in keeping with traditional combinatorial…”