Metric Scott analysis

Itai Ben Yaacov; Michal Doucha; Andre Nies; Todor Tsankov

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arXiv · 1407.7102

Metric Scott analysis

Itai Ben Yaacov·Michal Doucha·Andre Nies·Todor Tsankov

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Abstract

We develop an analogue of the classical Scott analysis for metric structures and infinitary continuous logic. Among our results are the existence of Scott sentences for metric structures and a version of the Lopez-Escobar theorem. We also derive some descriptive set theoretic consequences: most notably, that isomorphism on a class of separable structures is a Borel equivalence relation iff their Scott rank is uniformly bounded below $\omega_1$. Finally, we apply our methods to study the Gromov-Hausdorff distance between metric spaces and the Kadets distance between Banach spaces, showing that the set of spaces with distance $0$ to a fixed space is a Borel set.

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BibTeX RIS

Itai Ben Yaacov, Michal Doucha, Andre Nies, Todor Tsankov. 2014-07-26. Metric Scott analysis. https://arxiv.org/abs/1407.7102

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