RANDOMIZATIONS OF MODELS AS METRIC STRUCTURES

Confluentes Mathematici

JEROME KEISLER, H¹  BEN YAACOV, ITAϲ 

[1] Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison WI 53706, USA;Université de Lyon, CNRS, Université Claude Bernard Lyon 1, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France

关键词: Randomization;    metric structures;    continuous logic;    stable theories;   

DOI  :  10.1142/S1793744209000080

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

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.

【 授权许可】

Unknown