TY - JOUR
T1 - Generic separable metric structures
AU - Usvyatsov, Alexander
PY - 2008/8/15
Y1 - 2008/8/15
N2 - 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.
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.
KW - Generic structures
KW - Metric structures
KW - Urysohn space
UR - http://www.scopus.com/inward/record.url?scp=45849118677&partnerID=8YFLogxK
U2 - 10.1016/j.topol.2007.08.023
DO - 10.1016/j.topol.2007.08.023
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AN - SCOPUS:45849118677
SN - 0166-8641
VL - 155
SP - 1607
EP - 1617
JO - Topology and its Applications
JF - Topology and its Applications
IS - 14
ER -