Free and Hyperbolic Groups are not Equational
  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. 
Z. Sela
math.LO math.GR