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On perturbations of continuous structures. (English) Zbl 1191.03027

Summary: 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 \(\aleph_0\)-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 characterization of complete theories all of whose separable models are isomorphic up to arbitrarily small perturbations.

MSC:

03C90 Nonclassical models (Boolean-valued, sheaf, etc.)
03C35 Categoricity and completeness of theories
03C95 Abstract model theory
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References:

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