Diophantine geometry over groups VI: the elementary theory of a free group

By Z. Sela. 2006

222 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d2273248df9786ff64233211779d24095bfa60d5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

Citations in the corpus

Limit groups as limits of free groups: compactifying the set of free groups. (2004, background): “A positive answer to Tarski’s problem has been announced in [Sel01b] and [KM98c].”
Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness (2010, background): “Sela [25, 26, 27] on algebraic geometry over free groups.”
Limit groups as limits of free groups (2005, background): “A positive answer to Tarski’s problem has been announced in [Sel01b] and [KM98c].”
Unification theorems in algebraic geometry (2008, background): “…over G [4, 24, 25, 26, 47], groups universally equivalent to G [40, 13, 34], limit groups of G in the Grigorchuk-Gromov’s metric [10], in the theory of equations in groups [28, 38, 39, 24, 25, 26, 18], in group actions [8, 12, 35, 17, 14], in the solutions of Tarski problems [27, 48], etc.”
Homogeneity and prime models in torsion-free hyperbolic groups (2010, background): “Sela [38] and Kharlampovich and Myasnikov [11] show that nonabelian free groups have the same elementary theory and, in fact, the following more explicit description.”
Krull dimension of solvable groups (2008, background): “Notice, that the limit groups of free groups (known also as fully residually free groups, or freely discriminated groups, or ω-residually free groups) played a crucial part in a recent solution of the Tarski problems [35, 54], now they are one of the most actively studied classes of groups in geomet”
Determining Fuchsian groups by their finite quotients (2014, background): “A group Γ is termed a Poincaré duality group over a field F (or PDd(F) for short) if there is an integer d such that H∗(Γ;F) = H∗−d(Γ;F).”
Subgroups of direct products of limit groups (2007, background): “…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 group…”
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.”
Foliations for solving equations in groups: free, virtually free, and hyperbolic groups (2009, background): “Z. Sela, ‘The isomorphism problem for hyperbolic groups, I’, Ann. of Math.”