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On Σ11 equivalence relations with Borel classes of bounded rank1

Published online by Cambridge University Press:  12 March 2014

Ramez L. Sami
Ramez L. Sami*
Affiliation:
Cairo University, Cairo, Egypt
*
U.E.R. de Mathématique, Université Paris VII, Paris, France
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Abstract

In Baire space we define a sequence of equivalence relations ‹Ev ∣ v < , each Ev being with classes in + v + 1 and such that (i) Ev does not have perfectly many classes, and (ii) is countable iff < ω1. This construction can be extended cofinally in . A new proof is given of a theorem of Hausdorff on partitions of R into ω1 many sets.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 4 , December 1984 , pp. 1273 - 1283
Copyright
Copyright © Association for Symbolic Logic 1984

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Footnotes

1

The main results of this paper were presented at the Sixth International Congress of Logic, Methodology and the Philosophy of Science (Hannover, 1979).

References

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