arXiv subjects
Publications and source records attributed to Allison Wang.
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.
Let $E$ be a countable Borel equivalence relation on the space $\mathcal{E}_{\infty}$ of all infinite partitions of the natural numbers. We show that $E$ coincides with equality below a Carlson-Simpson generic element of $\mathcal{E}_{\infty}$. In contrast, we show that there is a hypersmooth equivalence relation on $\mathcal{E}_{\infty}$ which is Borel bireducible with $E_1$ on every Carlson-Simpson cube. Our arguments are classical and require no background in forcing.