3 research outputs found
On perturbations of Hilbert spaces and probability algebras with a generic automorphism
International audienceWe prove that , the theory of infinite dimensional Hilbert spaces equipped with a generic automorphism, is -stable up to perturbation of the automorphism, and admits prime models up to perturbation over any set. Similarly, , the theory of atomless probability algebras equipped with a generic automorphism is -stable up to perturbation. However, not allowing perturbation it is not even superstable
On perturbations of continuous structures
We give a general framework for the treatment of perturbations of types and
structures in continuous logic, allowing to specify which parts of the logic
may be perturbed. We prove that separable, elementarily equivalent structures
which are approximately -saturated up to arbitrarily small
perturbations are isomorphic up to arbitrarily small perturbations (where the
notion of perturbation is part of the data). As a corollary, we obtain a
Ryll-Nardzewski style characterisation of complete theories all of whose
separable models are isomorphic up to arbitrarily small perturbations