康托集上动力学的模型论性质

IF 0.6 3区数学 Q2 LOGIC

Notre Dame Journal of Formal Logic Pub Date : 2021-03-23 DOI:10.1215/00294527-2022-0022

Christopher J. Eagle, Alan Getz

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引用次数: 0

摘要

从可交换C*-代数的连续模型理论的角度研究了康托集合上的拓扑动力系统。在一些一般性的评论之后，我们将注意力集中在由Akin, Glasner和Weiss构造的Cantor集的一般同胚上。我们证明了这个同胚是其理论的素数模型。我们还表明，Akin、Glasner和Weiss使用的“一般”概念与Fräıssé理论中遇到的“一般”概念是不同的。

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Model-Theoretic Properties of Dynamics on the Cantor Set

We examine topological dynamical systems on the Cantor set from the point of view of the continuous model theory of commutative C*-algebras. After some general remarks we focus our attention on the generic homeomorphism of the Cantor set, as constructed by Akin, Glasner, and Weiss. We show that this homeomorphism is the prime model of its theory. We also show that the notion of “generic” used by Akin, Glasner, and Weiss is distinct from the notion of “generic” encountered in Fräıssé theory.

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来源期刊

Notre Dame Journal of Formal Logic MATHEMATICS-LOGIC

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Notre Dame Journal of Formal Logic, founded in 1960, aims to publish high quality and original research papers in philosophical logic, mathematical logic, and related areas, including papers of compelling historical interest. The Journal is also willing to selectively publish expository articles on important current topics of interest as well as book reviews.