Randomizations of models as metric structures

The notion of a randomization of a rst order structure was introduced by Keisler in the paper Randomizations of Models, Advances in Math. 1999. The idea was to form a new structure whose elements are random elements of the original rst 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 rst order theory is a complete theory in continuous logic that admits elimination of quantiers and has a natural set of axioms. We show that the randomization operation preserves the properties of being omega-categorical, omega-stable, and stable.