In this short note we prove that a definable set X over is superstable only if.

We give some lower bounds on the Shelah rank of varieties in the free group whose coordinate groups are hyperbolic towers.

We use hyperbolic towers to answer some model-theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the generic type $p_{0}$ but that there is a finitely generated model which omits $p^{}_{0}$. We exhibit a finitely generated model in which there are two maximal independent sets of realizations of the generic type which have different cardinalities. We also show that a free product of homogeneous groups is (...) not necessarily homogeneous. (shrink)