7 research outputs found

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

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    International audienceWe prove that IHSAIHS_A, the theory of infinite dimensional Hilbert spaces equipped with a generic automorphism, is ℵ0\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 ℵ0\aleph_0-stable up to perturbation. However, not allowing perturbation it is not even superstable

    On perturbations of continuous structures

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    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 ℵ0\aleph_0-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

    Stability and stable groups in continuous logic

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    We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity
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