Journal
TOPOLOGY AND ITS APPLICATIONS
Volume 155, Issue 14, Pages 1607-1617Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.topol.2007.08.023
Keywords
generic structures; metric structures; Urysohn space
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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. (C) 2008 Elsevier B.V. All rights reserved.
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