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Metric Scott analysis
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SYSNO ASEP 0476964 Document Type J - Journal Article R&D Document Type The record was not marked in the RIV Subsidiary J Článek ve WOS Title Metric Scott analysis Author(s) Ben Yaacov, I. (FR)
Doucha, Michal (MU-W) RID, SAI, ORCID
Nies, A. (FR)
Tsankov, T. (FR)Source Title Advances in Mathematics. - : Elsevier - ISSN 0001-8708
Roč. 318, October (2017), s. 46-87Number of pages 42 s. Language eng - English Country US - United States Keywords continuous logic ; infinitary logic ; Scott sentence Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support MU-W - RVO:67985840 UT WOS 000410020500002 EID SCOPUS 85026424504 DOI 10.1016/j.aim.2017.07.021 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2018
Number of the records: 1