The CH conjecture for MAD sigma-sets

A MAD family is a maximal almost disjoint family of infinite subsets of $\text{omega}$, and a subset $X\subseteq 2^\omega$ is a sigma-set if for every Borel set $B\subseteq 2^\omega$ there is a $G_\delta$ set $G$ such that $B\cap X=G\cap X$. CH conjecture. The continuum hypothesis implies that there exists a MAD sigma-set. The statement is motivated by the consistency result that a MAD sigma-set of size the continuum can exist with arbitrary prescribed cardinal arithmetic, together with large-cardinal absoluteness results; its status is presented in the source as conjectural.