Ampleness in the free group
  We show that the theory of the free group -- and more generally the theory of any torsion-free hyperbolic group -- is $n$-ample for any $n\geq 1$. We give also an explicit description of the imaginary algebraic closure in free groups. 
Abderezak Ould Houcine, Katrin Tent
math.GR math.LO