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Preprint Number 160

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160. Itaï Ben Yaacov, H. Jerome Keisler
Randomizations of models as metric structures

Submission date: 24 January 2009.


The paper \cite{Ke} introduced the notion of a randomization of a first order structure CM. The idea was to form a new structure whose elements are random elements of CM. In this paper we treat randomizations as continuous structures in the sense of the paper \cite{BU}. In this setting, the results of \cite{Ke} show that if T is the complete theory of CM, the theory T^R of randomizations of CM is a complete theory in continuous logic which admits elimination of quantifiers and has a natural set of axioms. We show that T^R is ω-categorical, ω-stable or stable as a continuous theory if and only if T is ω-categorical, ω-stable or stable as a first order theory.

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