Randomizations of models as metric structures

Itaï Ben Yaacov (1) , H. Jerome Keisler (2)

1 ICJ - Institut Camille Jordan
2 Department of Mathematics [Madison]

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.

Mots clés: randomization; metric structures; continuous logic; stable theories

Domaines: Logique [math.LO]

Itaï Ben Yaacov, H. Jerome Keisler. Randomizations of models as metric structures. Confluentes Mathematici, 2009, 1 (2), pp.197-223. ⟨10.1142/S1793744209000080⟩. ⟨hal-00351833v2⟩