I don't known the correct credit for the following: every non-empty $\Pi^1\_1$ set of reals contains some $X \in L\_{\alpha}$ for some $X$-recursive $\alpha$. (Addison-Kondo?)


So, my question is: what is the least $\beta$, s.t. $\mathcal{P}(\omega) \cap L\_\beta$ is a basis for all non-empty $\Pi^1\_1$ sets?



To find an element of a  $\Pi^1_1$  set
I can't access the full paper at the moment, but I'm pretty sure this is exactly the question addressed in the paper "A Note on the Kondo-Addison Theorem" by D. Guaspari 


