  Sabok showed that the set of codes for $G_\delta$ Ramsey positive subsets of
$[\omega]^\omega$ is $\mathbf{\Sigma}^1_2$-complete. We extend this result by
providing sufficient conditions for the set of codes for $G_\delta$ Ramsey
positive subsets of an arbitrary topological Ramsey space to be
$\mathbf{\Sigma}^1_2$-complete.
