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A modification of Louveau and Velickovic's construction for $F_\sigma$-ideals

Author: Krzysztof Mazur
Journal: Proc. Amer. Math. Soc. 128 (2000), 1475-1479
MSC (1991): Primary 04A15; Secondary 04A20
Published electronically: February 7, 2000
MathSciNet review: 1626442
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We show that the construction of Louveau and Velickovic can be modified to obtain an embedding of $([\omega]^\omega,\subset^*)$ into the preorder $(F_\sigma\textit{-ideals},\le)$ where $\le$ is the relation of Borel reducibility.

References [Enhancements On Off] (What's this?)

  • 1. L. Harrington, A. S. Kechris and A. Louveau, A Glimm-Effros dichotomy for Borel Equivalence relations, J. Amer. Math. Soc., 3(4) p. 903-927, 1990. MR 91h:28023
  • 2. A. Louveau and B. Velickovic, A note on Borel equivalence relations, Proc. Amer. Math. Soc., p. 120, 255-259, 1994. MR 94f:54076
  • 3. S. Solecki, Analytic Ideals, Bull. Symb. Logic. 2 (1996), p. 339-348. MR 97i:04002

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Additional Information

Krzysztof Mazur
Affiliation: Department of Mathematics, University of Warsaw, 02-097, Warsaw, Banacha 2, Poland

Keywords: $F_\sigma$-ideal, Borel reducibility, reducing function
Received by editor(s): December 9, 1997
Received by editor(s) in revised form: January 6, 1998, and May 4, 1998
Published electronically: February 7, 2000
Additional Notes: The author passed away on October 30, 1998
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2000 American Mathematical Society