Model-Theoretic Properties of Dynamics on the Cantor Set

IF 0.6 3区 数学 Q2 LOGIC
Christopher J. Eagle, Alan Getz
{"title":"Model-Theoretic Properties of Dynamics on the Cantor Set","authors":"Christopher J. Eagle, Alan Getz","doi":"10.1215/00294527-2022-0022","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Notre Dame Journal of Formal Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/00294527-2022-0022","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0

Abstract

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.
康托集上动力学的模型论性质
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
1.00
自引率
14.30%
发文量
14
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信