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Cantor minimal systems from a descriptive perspective
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Kaya, Burak. Cantor minimal systems from a descriptive perspective. Retrieved from https://doi.org/doi:10.7282/T3WD42Q2

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TitleCantor minimal systems from a descriptive perspective
NameKaya, Burak (author); Thomas, Simon (chair); Cherlin, Gregory (internal member); Sargsyan, Grigor (internal member); Hamkins, Joel David (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2016
Other Date2016-05 (degree)
SubjectMathematics, Descriptive set theory
Extent1 online resource (v, 85 p. : ill.)
DescriptionIn recent years, the study of the Borel complexity of naturally occurring classification problems has been a major focus in descriptive set theory. This thesis is a contribution to the project of analyzing the Borel complexity of the topological conjugacy relation on various Cantor minimal systems. We prove that the topological conjugacy relation on pointed Cantor minimal systems is Borel bireducible with the Borel equivalence relation $Delta_{mathbb{R}}^+$. As a byproduct of our analysis, we also show that $Delta_{mathbb{R}}^+$ is a lower bound for the Borel complexity of the topological conjugacy relation on Cantor minimal systems. The other main result of this thesis concerns the topological conjugacy relation on Toeplitz subshifts. We prove that the topological conjugacy relation on Toeplitz subshifts with separated holes is a hyperfinite Borel equivalence relation. This result provides a partial affirmative answer to a question asked by Sabok and Tsankov. As pointed Cantor minimal systems are represented by properly ordered Bratteli diagrams, we also establish that the Borel complexity of equivalence of properly ordered Bratteli diagrams is $Delta_{mathbb{R}}^+$.
NotePh.D.
NoteIncludes bibliographical references
Noteby Burak Kaya
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3WD42Q2
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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