  We prove that the set of limit groups is recursive, answering a question of
Delzant. One ingredient of the proof is the observation that a finitely
presented group with local retractions (a la Long and Reid) is coherent and,
furthermore, there exists an algorithm that computes presentations for finitely
generated subgroups. The other main ingredient is the ability to
algorithmically calculate centralizers in relatively hyperbolic groups.
Applications include the existence of recognition algorithms for limit groups
and free groups.
