Ampleness in the free group

Abderezak Ould Houcine (1, 2) , Katrin Tent (3)

1 ICJ - Institut Camille Jordan
2 Institut de Mathématiques [Mons]
3 Université de Munster

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.

Mots clés: free groups; torsion-free hyperbolic groups; n-ample; ampleness

Domaines: Théorie des groupes [math.GR]; Logique [math.LO]

Abderezak Ould Houcine, Katrin Tent. Ampleness in the free group. 2012. ⟨hal-00694506⟩