How to construct a real Baire function of class $\alpha$ which is not in the class $\alpha-1$, where $\alpha\in \mathbb{N}$? I believe the solution to this problem is equivalent to constructing a $\Sigma_{\alpha+1}^0$ set which is not in $\Sigma_{\alpha}^0$ (using characteristic functions), any such construction in $\mathbb{R}$?
2026-03-29 14:58:49.1774796329
Constructing Baire functions of some class which are not of the previous class
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