Submission date: 23 April 2012.

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.

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Full text arXiv 1204.5075: pdf, ps.