Metric Scott analysis

0476964 - MÚ 2018 US eng J - Journal Article
Ben Yaacov, I. - Doucha, Michal - Nies, A. - Tsankov, T.
Metric Scott analysis.
Advances in Mathematics. Roč. 318, October (2017), s. 46-87. ISSN 0001-8708. E-ISSN 1090-2082
Institutional support: RVO:67985840
Keywords : continuous logic * infinitary logic * Scott sentence
OECD category: Pure mathematics
Impact factor: 1.372, year: 2017
http://www.sciencedirect.com/science/article/pii/S0001870816309896?via%3Dihub

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 López-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 omega1. 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.
Permanent Link: http://hdl.handle.net/11104/0273370