There is no bound on Borel classes of the graphs in the Luzin-Novikov theorem

P. Holicky, M. Zeleny

We show that for every ordinal $\alpha \in [1,{\omega }_1)$ there is a closed set $F\subset 2^{\omega }\times {\omega }^{\omega }$ such that for every $x\in 2^{\omega }$ the section $\{y\in {\omega }^{\omega };(x,y)\in F\}$ is a two-poin…