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arXiv · 0810.4086

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

Itaï Ben Yaacov·Alexander Berenstein
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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.

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Itaï Ben Yaacov, Alexander Berenstein. 2009-06-02. On perturbations of Hilbert spaces and probability algebras with a generic automorphism. https://doi.org/10.4115/jla.2009.1.7

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