Ampleness in the free group

Abstract

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 $n\ge 1$. We give also an explicit description of the imaginary algebraic closure in free groups.

References in corpus (8)

• Limit groups as limits of free groups: compactifying the set of free groups
• Homogeneity in the free group
• JSJ decompositions: definitions, existence, uniqueness. I: The JSJ deformation space
• Diophantine Geometry over Groups IX: Envelopes and Imaginaries
• Diophantine Geometry over Groups X: The Elementary Theory of Free Products of Groups
• On groups and fields interpretable in torsion-free hyperbolic groups
• Homogeneity and prime models in torsion-free hyperbolic groups
• Algebraic & definable closure in free groups

Cited by in corpus (4)

• On groups and fields interpretable in torsion-free hyperbolic groups
• A note on ampleness in the theory of non abelian free groups
• On ampleness and pseudo-Anosov homeomorphisms in the free group
• Fields interpretable in the free group