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

Itaï Ben Yaacov (1) , Alexander Berenstein (1, 2)

1 ICJ - Institut Camille Jordan
2 UNIANDES - Universidad de los Andes [Bogota]

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.

Mots clés: Hilbert space; probability algebra; automorphism; perturbation; stability

Domaines: Logique [math.LO]

Itaï Ben Yaacov, Alexander Berenstein. On perturbations of Hilbert spaces and probability algebras with a generic automorphism. Journal of Logic and Analysis, 2009, 1 (7), pp.1-18. ⟨10.4115/jla.2009.1.7⟩. ⟨hal-00332963v2⟩