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On analytic filters and prefilters

Published online by Cambridge University Press:  12 March 2014

Samy Zafrany
Samy Zafrany*
Affiliation:
Department of Mathematics and Computer Science, Ben Gurion University of the Negev, Beer Sheva, Israel
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Abstract

We show that every analytic filter is generated by a prefilter, every filter is generated by a prefilter, and if is a prefilter then the filter generated by it is also . The last result is unique for the Borel classes, as there is a -complete prefilter P such that the filter generated by it is -complete. Also, no complete coanalytic filter is generated by an analytic prefilter. The proofs use König's infinity lemma, a normal form theorem for monotone analytic sets, and Wadge reductions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 1 , March 1990 , pp. 315 - 322
Copyright
Copyright © Association for Symbolic Logic 1990

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References

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