Diophantine geometry over groups VIII: Stability

By Z. Sela. 2006

70 citations recorded by the source corpus.

This paper is the eighth in a sequence on the structure of sets of solutions to systems of equations in free and hyperbolic groups, projections of such sets (Diophantine sets), and the structure of denable sets over free and hyperbolic groups. In this eighth paper we use a modication of the sieve procedure, which was used in proving quantier elimination in the theory of a free group, to prove that free and torsion-free (Gromov) hyperbolic groups are stable. In the

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7309a2f0833f3b45030ca10eca0813f812709bd9

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Citations in the corpus

Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, result): “superstability may be considered, in a very rough sense, as an indication of logical complexity of the theory. For other results about stable and superstable groups we refer to the survey [147]. Sela [136] showed that free groups and, more generally, torsion free hyperbolic groups are stable. On the”
Definably amenable NIP groups (2015, background): “e, if G(M)is amenable as a discrete group, then it is deﬁnably amenable since we have such a measure on all subsets, not just the deﬁnable ones, but the converse need not hold (e.g. deep work of Sela [Sel13] demonstrates that any non-commutative free group, viewed as a ﬁrst-order structure in the gr”