Geodesic
Randomizations of models as metric structures
Confluentes Mathematici, Tome 1 (2009) no. 2, pp. 197-223

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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.

Publié le :
DOI : 10.1142/S1793744209000080

Ben Yaacov, Itaï 1 ; Keisler, H. Jerome 1

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Ben Yaacov, Itaï; Keisler, H. Jerome. Randomizations of models as metric structures. Confluentes Mathematici, Tome 1 (2009) no. 2, pp. 197-223. doi: 10.1142/S1793744209000080

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