Diophantine geometry over groups VIII: Stability

Z. Sela*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

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 quantifier elimination in the theory of a free group, to prove that free and torsion-free (Gromov) hyperbolic groups are stable.

Original languageAmerican English
Pages (from-to)787-868
Number of pages82
JournalAnnals of Mathematics
Volume177
Issue number3
DOIs
StatePublished - 2013

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