RANDOMIZATIONS OF MODELS AS METRIC STRUCTURES

Q4 Mathematics

Confluentes Mathematici Pub Date : 2009-01-11 DOI:10.1142/S1793744209000080

I. Yaacov, H. Keisler

引用次数: 43

Abstract

The notion of a randomization of a rst order structure was introduced by Keisler in the paper Randomizations of Models, Advances in Math. 1999. The idea was to form a new structure whose elements are random elements of the original rst 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 rst order theory is a complete theory in continuous logic that admits elimination of quantiers 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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作为度量结构的模型随机化

一阶结构随机化的概念是由Keisler在《数学进展》1999年发表的论文《模型的随机化》中提出的。我们的想法是形成一个新的结构，它的元素是原始一阶结构的随机元素。在本文中，我们将随机化视为Ben Yaacov和Usvyatsov意义上的连续结构。在这种情况下，先前的结果表明，完全一阶理论的随机化是连续逻辑中允许消去量子数并具有自然公理集的完全理论。我们证明了随机化操作保留了ω -分类，ω -稳定和稳定的性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.