English

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

Logic 2009-07-01 v2

Abstract

We prove that IHSAIHS_A, the theory of infinite dimensional Hilbert spaces equipped with a generic automorphism, is 0\aleph_0-stable up to perturbation of the automorphism, and admits prime models up to perturbation over any set. Similarly, APrAAPr_A, the theory of atomless probability algebras equipped with a generic automorphism is 0\aleph_0-stable up to perturbation. However, not allowing perturbation it is not even superstable.

Keywords

Cite

@article{arxiv.0810.4086,
  title  = {On perturbations of Hilbert spaces and probability algebras with a generic automorphism},
  author = {Itaï Ben Yaacov and Alexander Berenstein},
  journal= {arXiv preprint arXiv:0810.4086},
  year   = {2009}
}