On perturbations of continuous structures

Abstract

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 characterisation of complete theories all of whose separable models are isomorphic up to arbitrarily small perturbations.

References in corpus (6)

• Topometric spaces and perturbations of metric structures
• Model theory of probability spaces with an automorphism
• Model-theoretic independence in the Banach lattices $L_p(\mu )$
• Continuous first order logic for unbounded metric structures
• On perturbations of Hilbert spaces and probability algebras with a generic automorphism
• On supersimplicity and lovely pairs of cats

Cited by in corpus (7)

• Topometric spaces and perturbations of metric structures
• Modular functionals and perturbations of Nakano spaces
• Continuous first order logic for unbounded metric structures
• Lipschitz functions on topometric spaces
• On perturbations of Hilbert spaces and probability algebras with a generic automorphism
• ${\aleph }_0$-categorical Banach spaces contain ${\ell }_p$ or $c_0$
• Topometric characterization of type spaces in continuous logic