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Pré-Publication, Document De Travail Année : 2008

On perturbations of Hilbert spaces and probability algebras with a generic automorphism

Résumé

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.
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Dates et versions

hal-00332963 , version 1 (22-10-2008)
hal-00332963 , version 2 (02-06-2009)

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Citer

Itaï Ben Yaacov, Alexander Berenstein. On perturbations of Hilbert spaces and probability algebras with a generic automorphism. 2008. ⟨hal-00332963v1⟩

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