2 problems

Todorčević's conjecture. It is relatively consistent with $\mathsf{ZFC}$ that if $X$ is a regular $\mathsf{HL}$ space, then $\mathsf{OGA}(X)$ holds.

Todorčević's conjecture. It is relatively consistent with $\mathsf{ZFC}$ that if $X$ is a regular space with no uncountable discrete subspace, then $\mathsf{OGA}(X)$ holds.