Selivanovski hard sets are hard
Volume 228 / 2015
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.
