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Some results on projective equivalence relations


Li, Xuhua (1998) Some results on projective equivalence relations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/pn2n-7z61.


We construct a ∏11 equivalence relation E on ωω for which there is no largest E-thin, E-invariant ∏11 subset of ωω. Then we lift our result to the general case. Namely, we show that there is a ∏12n+1 equivalence relation for which there is no largest E-thin, E-invariant ∏12n+1 set under projective determinacy. This answers an open problem raised in Kechris [Ke2].

Our second result in this thesis is a representation for thin ∏13 equivalence relations on uω. Precisely, we show that for each thin ∏13 equivalence relation E on uω, there is a Δ13 in the codes map p: ωω → uω and a ∏13 in the codes equivalence relation e on uω such that for all real numbers x and y,

xEy ↔ (p(x),p(y))∈ e

This lifts Harrington's result about thin ∏11 equivalence relations to thin ∏13 equivalence relations.

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.
Thesis Committee:
  • Ramakrishnan, Dinakar
  • Luxemburg, W. A. J.
Defense Date:22 June 1997
Record Number:CaltechTHESIS:01202017-113604553
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10016
Deposited By: Benjamin Perez
Deposited On:23 Jan 2017 20:48
Last Modified:09 Nov 2022 19:19

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