Randomizations of models as metric structures
Confluentes Mathematici, Volume 1 (2009) no. 2, pp. 197-223.

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.

Published online:
DOI: 10.1142/S1793744209000080
Itaï Ben Yaacov 1; H. Jerome Keisler 1

1
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Itaï Ben Yaacov; H. Jerome Keisler. Randomizations of models as metric structures. Confluentes Mathematici, Volume 1 (2009) no. 2, pp. 197-223. doi : 10.1142/S1793744209000080. https://cml.centre-mersenne.org/articles/10.1142/S1793744209000080/

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