# Basis theorem (due to Solovay?)

I'm finishingg up my bibliography and I'm looking for a reference for the statement that, working in $L(\R)$, the $\Delta^2_1$ sets form a basis for the $\Sigma^2_1$ predicates. I believe that it is due to Solovay.

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I do not think it appears explicitly in a paper by Solovay. It should date back to 1976 at the latest, which is when Kechris and Solovay observed that not all $\Pi^2_1$ sets can be uniformized if $V=L(\mathbb R)$ and choice fails (see section 30 in Kanamori's book).