Diophantine geometry over groups VIII: Stability

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 definable sets over free and hyperbolic groups. In this eighth paper we use a modification 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.

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      author={Sela, Z.},
      TITLE={Diophantine geometry over groups {IX: E}nvelopes and imaginaries},
      NOTE={preprint},
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     }

Authors

Z. Sela

Department of Mathematics
The Hebrew University of Jerusalem
Jerusalem 91904
Israel