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Hurewicz test sets for generalized separation and reduction



We prove a Hurewicz-type theorem for generalized separation: we present a method which allows us to test if for a sequence of Borel sets (Ai)i > ω satisfying there is a sequence (Bi)i < ω of Π0ξ sets such that or not. We also prove an analogous result for generalized reduction. The results of the paper are motivated by a Hurewicz-type theorem of A. Louveau and J. Saint Raymond on ordinary separation of analytic sets.



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Hurewicz test sets for generalized separation and reduction



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