TY - JOUR
T1 - Diophantine geometry over groups VIII
T2 - Stability
AU - Sela, Z.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84879324324&partnerID=8YFLogxK
U2 - 10.4007/annals.2013.177.3.1
DO - 10.4007/annals.2013.177.3.1
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AN - SCOPUS:84879324324
SN - 0003-486X
VL - 177
SP - 787
EP - 868
JO - Annals of Mathematics
JF - Annals of Mathematics
IS - 3
ER -