Generic separable metric structures

Alexander Usvyatsov

doi:10.1016/j.topol.2007.08.023

Generic separable metric structures

Alexander Usvyatsov

Research output: Contribution to journal › Article › peer-review

Abstract

We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure theoretic sense. In particular, it gives a new perspective on Vershik's theorems on genericity and randomness of Urysohn's space among separable metric spaces.

Original language	English
Pages (from-to)	1607-1617
Number of pages	11
Journal	Topology and its Applications
Volume	155
Issue number	14
DOIs	https://doi.org/10.1016/j.topol.2007.08.023
State	Published - 15 Aug 2008
Externally published	Yes

Keywords

Generic structures
Metric structures
Urysohn space

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10.1016/j.topol.2007.08.023

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AB - We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure theoretic sense. In particular, it gives a new perspective on Vershik's theorems on genericity and randomness of Urysohn's space among separable metric spaces.

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Generic separable metric structures

Abstract

Keywords

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