Submission date: 24 January 2009.

Abstract:

We prove that IHS_A, the theory of infinite dimensional Hilbert spaces equipped with a generic automorphism, is \aleph_0-stable up to perturbation of the automorphism, and admits prime models up to perturbation over any set. Similarly, APr_A, the theory of atomless probability algebras equipped with a generic automorphism is \aleph_0-stable up to perturbation. However, not allowing perturbation it is not even superstable.

Mathematics Subject Classification:

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