作为度量结构的模型的随机化
Randomizations of models as metric structures
摘要：
一阶结构的随机化的概念是由Keisler在论文Randomizing a Model，Advances in Math.1999中引入的。这个想法是形成一个新的结构，其元素是原始一阶结构的随机元。在本文中，我们把随机化作为连续结构的意义上的Ben Yaacov和Usvyatsov。在这种情况下，早期的结果表明，一个完整的一阶理论的随机化是一个完整的理论，在连续逻辑，承认量词消去，并有一个自然的公理集。我们证明了随机化操作保持了omega-分类，omega-稳定和稳定的性质。
英文摘要：
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.
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