2 problems

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Todorčević's consistency conjecture for regular hereditary Lindelöf spaces
Todorčević's conjecture. It is relatively consistent with $\mathsf{ZFC}$ that if $X$ is a regular $\mathsf{HL}$ space, then $\mathsf{OGA}(X)$ holds.
Conjectureopenhereditary-lindelof open-graph-axiom set-theoretic-topologyarXiv posted 2 days ago
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Todorčević's consistency conjecture for regular spaces of countable spread
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.
Conjectureopenopen-graph-axiom set-theoretic-topologyarXiv posted 2 days ago

Todorčević's consistency conjecture for regular hereditary Lindelöf spaces