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Hurewicz test sets for generalized separation and reduction

  • TAMÁS MÁTRAI (a1)

Abstract

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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[1]Debs, G. and Raymond, J. Saint. Effective refining of Borel coverings. Preprint.
[2]Kechris, A. S.. Classical Descriptive Set Theory. Graduate Texts in Mathematics 156 (Springer-Verlag, 1994).
[3]Louveau, A. and Raymond, J. Saint. Borel Classes and Closed Games: Wadge-type and Hurewicz-type Results. Trans. Amer. Math. Soc., 304, No. 2 (1987) 431467.
[4]Mátrai, T.. Hurewicz tests: separating and reducing analytic sets the conscious way. PhD Thesis (Central European University, 2005).
[5]Mátrai, T.. On the closure of Baire classes under transfinite convergences. Fund. Math. 183 (2004), 157168.
[6]Moschovakis, Y.. Descriptive Set Theory. Studies in Logic and the Foundations of Mathematics, Volume 100 (North-Holland Publishing Co., 1980).

Hurewicz test sets for generalized separation and reduction

  • TAMÁS MÁTRAI (a1)

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