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Topics in descriptive set theory related to equivalence relations, complex borel and analytic sets


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. doi:10.7907/vva8-1959.


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 ∏03-complete and the set of all sequences of entire functions whose orders converge to α is ∏05-complete. We also prove that given any line in the plane and any cardinal number 1 ≤ n ≤ N0, the set of continuous paths in the plane tracing curves which admit at least n tangents parallel to the given line is Σ11-complete and the set of differentiable paths of class C2 in the plane admitting a canonical parameter in [0,1] and tracing curves which have at least n vertices is also Σ11-complete.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kechris, Alexander S. (advisor)
  • Wolff, Thomas H. (co-advisor)
Thesis Committee:
  • Kechris, Alexander S. (chair)
  • Luxemburg, W. A. J.
  • Wolff, Thomas H.
  • Gao, S.
Defense Date:13 April 1999
Funding AgencyGrant Number
NSFDMS 9619880
Record Number:CaltechTHESIS:01232017-134252080
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10021
Deposited By: Benjamin Perez
Deposited On:23 Jan 2017 22:24
Last Modified:09 Nov 2022 19:19

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