Complexity of Ramsey null sets

We show that the set of codes for Ramsey positive analytic sets is Σ21-complete. This is an analogue of a theorem of Hurewicz saying that the set of uncountable compact subsets of an uncountable Polish space is Σ11-complete. As a corollary, we get that the σ-ideal of Ramsey null sets is not ZFC-correct, which answers a question of Ikegami, Pawlikowski and Zapletal.