The notion of a randomization of a first-order structure was introduced by Keisler in the paper Randomizing a Model, Advances in Math. 1999. The idea was to form a new structure whose elements are random elements of the original first-order structure. In this paper we treat randomizations as continuous structures in the sense of Ben Yaacov and Usvyatsov. In this setting, the earlier results show that the randomization of a complete first-order theory is a complete theory in continuous logic that admits elimination of quantifiers and has a natural set of axioms. We show that the randomization operation preserves the properties of being omega-categorical, omega-stable, and stable.
@article{CML_2009__1_2_197_0,
author = {Ben Yaacov, Ita{\"\i} and Keisler, H. Jerome},
title = {Randomizations of models as metric structures},
journal = {Confluentes Mathematici},
pages = {197--223},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {1},
number = {2},
year = {2009},
doi = {10.1142/S1793744209000080},
language = {en},
url = {http://archive.numdam.org/articles/10.1142/S1793744209000080/}
}
TY - JOUR AU - Ben Yaacov, Itaï AU - Keisler, H. Jerome TI - Randomizations of models as metric structures JO - Confluentes Mathematici PY - 2009 SP - 197 EP - 223 VL - 1 IS - 2 PB - World Scientific Publishing Co Pte Ltd UR - http://archive.numdam.org/articles/10.1142/S1793744209000080/ DO - 10.1142/S1793744209000080 LA - en ID - CML_2009__1_2_197_0 ER -
%0 Journal Article %A Ben Yaacov, Itaï %A Keisler, H. Jerome %T Randomizations of models as metric structures %J Confluentes Mathematici %D 2009 %P 197-223 %V 1 %N 2 %I World Scientific Publishing Co Pte Ltd %U http://archive.numdam.org/articles/10.1142/S1793744209000080/ %R 10.1142/S1793744209000080 %G en %F CML_2009__1_2_197_0
Ben Yaacov, Itaï; Keisler, H. Jerome. Randomizations of models as metric structures. Confluentes Mathematici, Tome 1 (2009) no. 2, pp. 197-223. doi : 10.1142/S1793744209000080. http://archive.numdam.org/articles/10.1142/S1793744209000080/
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