Randomizations of models as metric structures

Abstract

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.

References in corpus (1)

• On theories of random variables

Cited by in corpus (12)

• On theories of random variables
• Keisler measures in the wild
• Pseudofinite and pseudocompact metric structures
• Isometry group of Borel randomizations
• Independence relations in randomizations
• Generic Stability and Modes of Convergence
• Vaught's Two-Cardinal Theorem and Quasi-Minimality in Continuous Logic
• Algebraic Independence Relations in Randomizations
• Glivenko-Cantelli classes and NIP formulas
• Definable closure in randomizations
• Generically stable and smooth measures in NIP theories
• Finding generically stable measures