In 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 $Delta_{mathbb{R}}^+$.
Subject (authority = RUETD)
Topic
Mathematics
Subject (authority = ETD-LCSH)
Topic
Descriptive set theory
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
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ETD_7097
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (v, 85 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Burak Kaya
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
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Rutgers University. Graduate School - New Brunswick
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License
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