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On analytic filters and prefilters
Published online by Cambridge University Press: 12 March 2014
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.
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- Research Article
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- Copyright © Association for Symbolic Logic 1990
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