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

Author(s): Krzysztof Mazur
Journal: Proc. Amer. Math. Soc. 128 (2000), 1475-1479.
MSC (1991): Primary 04A15; Secondary 04A20
Posted: February 7, 2000
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Abstract:

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:

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
Email: krzymaz@mimuw.edu.pl

DOI: 10.1090/S0002-9939-00-05061-9
PII: S 0002-9939(00)05061-9
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
Posted: February 7, 2000
Additional Notes: The author passed away on October 30, 1998
Communicated by: Carl G. Jockusch, Jr.
Copyright of article: Copyright 2000, American Mathematical Society


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