## Citation

Sofronidis, Nikolaos Efstathiou
(1999)
*Topics in descriptive set theory related to equivalence relations, complex borel and analytic sets.*
Dissertation (Ph.D.), California Institute of Technology.
http://resolver.caltech.edu/CaltechTHESIS:01232017-134252080

## Abstract

The purpose of this doctoral dissertation is first to show that certain kinds of invariants for measures, self-adjoint and unitary operators are as far from complete as possible and second to give new natural examples of complex Borel and analytic sets originating from Analysis and Geometry.

The dissertation is divided in two parts.

In the first part we prove that the measure equivalence relation and certain
of its most characteristic subequivalence relations are generically S_{∞}-
ergodic and unitary conjugacy of self-adjoint and unitary operators is generically
turbulent.

In the second part we prove that for any 0 ≤ α < ∞, the set of entire
functions whose order is equal to α is ∏^{0}_{3}-complete and the set of all sequences
of entire functions whose orders converge to α is ∏^{0}_{5}-complete. We also prove
that given any line in the plane and any cardinal number 1 ≤ n ≤ N_{0}, the
set of continuous paths in the plane tracing curves which admit at least n
tangents parallel to the given line is Σ^{1}_{1}-complete and the set of differentiable
paths of class C^{2} in the plane admitting a canonical parameter in [0,1] and
tracing curves which have at least n vertices is also Σ^{1}_{1}-complete.

Item Type: | Thesis (Dissertation (Ph.D.)) | ||||
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Subject Keywords: | Mathematics | ||||

Degree Grantor: | California Institute of Technology | ||||

Division: | Physics, Mathematics and Astronomy | ||||

Major Option: | Mathematics | ||||

Thesis Availability: | Restricted to Caltech community only | ||||

Research Advisor(s): | - Kechris, Alexander S. (advisor)
- Wolff, Thomas H. (co-advisor)
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Thesis Committee: | - Kechris, Alexander S. (chair)
- Luxemburg, W. A. J.
- Wolff, Thomas H.
- Gao, S.
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Defense Date: | 13 April 1999 | ||||

Funders: |
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Record Number: | CaltechTHESIS:01232017-134252080 | ||||

Persistent URL: | http://resolver.caltech.edu/CaltechTHESIS:01232017-134252080 | ||||

Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||

ID Code: | 10021 | ||||

Collection: | CaltechTHESIS | ||||

Deposited By: | Benjamin Perez | ||||

Deposited On: | 23 Jan 2017 22:24 | ||||

Last Modified: | 23 Jan 2017 22:24 |

## Thesis Files

PDF
- Final Version
Restricted to Caltech community only See Usage Policy. 22Mb |

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