  We show that the set of codes for Ramsey positive analytic sets is
$\mathbf{\Sigma}^1_2$-complete. This is a one projective-step higher analogue
of the Hurewicz theorem saying that the set of codes for uncountable analytic
sets is $\mathbf{\Sigma}^1_1$-complete. This shows a close resemblance between
the Sacks forcing and the Mathias forcing. In particular, we get that the
$\sigma$-ideal of Ramsey null sets is not ZFC-correct. This solves a problem
posed by Ikegami, Pawlikowski and Zapletal.
