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

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

2008-10-22

arxiv.org/abs/0810.4086v2

Journal of Logic and Analysis 1, 7 (2009) 1-18

Mathematics

Logic

Scientific paper

10.4115/jla.2009.1.7

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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