2008/02/01 by Alexander Usvyatsov, Usvyatsov, Alexander
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #math.GN #math.LO
paper · pdf · doi:10.48550/arxiv.0802.0156
arxiv created 2008/02/01 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.