Randomizations of models as metric structures

Details Randomizations of models as metric structures Randomizations of models as metric structures

2009-01-12

arxiv.org/abs/0901.1583v2

Confluentes Mathematici 1, 2 (2009) 197-223

Mathematics

Logic

Scientific paper

10.1142/S1793744209000080

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.

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