The complexity of topological conjugacy of pointed Cantor minimal systems

被引:0
|
作者
Burak Kaya
机构
[1] Rutgers University,Department of Mathematics
来源
Archive for Mathematical Logic | 2017年 / 56卷
关键词
Borel complexity; Topological conjugacy; Cantor minimal systems; Bratteli diagrams; Primary 03E15; Secondary 37B05;
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摘要
In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal systems from the point of view of descriptive set theory. We prove that the topological conjugacy relation on pointed Cantor minimal systems is Borel bireducible with the Borel equivalence relation ΔR+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta _{\mathbb {R}}^+$$\end{document} on RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^{{\mathbb {N}}}$$\end{document} defined by xΔR+y⇔{xi:i∈N}={yi:i∈N}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x \varDelta _{\mathbb {R}}^+y \Leftrightarrow \{x_i{:}\,i \in {\mathbb {N}}\}=\{y_i{:}\,i \in {\mathbb {N}}\}$$\end{document}. Moreover, we show that ΔR+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta _{\mathbb {R}}^+$$\end{document} is a lower bound for the Borel complexity of topological conjugacy of Cantor minimal systems. Finally, we interpret our results in terms of properly ordered Bratteli diagrams and discuss some applications.
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页码:215 / 235
页数:20
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