Free and Hyperbolic Groups are not Equational

Abstract

We give an example of a definable set in every free or torsion-free (non-elementary) hyperbolic group that is not in the Boolean algebra of equational sets. Hence, the theories of free and torsion-free (non-elementary) hyperbolic groups are not equational in the sense of G. Srour.

References in corpus (1)

• Diophantine Geometry over Groups IX: Envelopes and Imaginaries