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Selivanovski hard sets are hard

Volume 228 / 2015

Janusz Pawlikowski Fundamenta Mathematicae 228 (2015), 17-25 MSC: Primary 03E15; Secondary 54H05. DOI: 10.4064/fm228-1-2

Abstract

Let $H\subseteq Z\subseteq 2^{\omega }$. For $n\ge 2$, we prove that if Selivanovski measurable functions from $2^{\omega }$ to $Z$ give as preimages of $H$ all $\boldsymbol {\Sigma }_{n}^{1}$ subsets of $2^{\omega }$, then so do continuous injections.

Authors

  • Janusz PawlikowskiDepartment of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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