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Preprint Number 1871

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1871. James Hanson
Approximate Isomorphism of Metric Structures

Submission date: 1 November 2020


We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov and by Ben Yaacov, Berenstein, Henson, and Usvyatsov, which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach-Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation systems and semantically by certain elementary classes of two-sorted structures that witness approximate isomorphism.

Mathematics Subject Classification: 03C66, 03C75, 03C15

Keywords and phrases:

Full text arXiv 2011.00588: pdf, ps.

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