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

Abstract

We prove that $IH{S}_A$, 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, $AP{r}_A$, 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.

References in corpus (4)

• Topometric spaces and perturbations of metric structures
• Modular functionals and perturbations of Nakano spaces
• Model theory of probability spaces with an automorphism
• On supersimplicity and lovely pairs of cats

Cited by in corpus (1)

• Topometric spaces and perturbations of metric structures