Strong nesting characterization of Pi-one-three-MI
Prove or refute the equivalence between Pi-one-three monotone induction over the reals of L-beta and the existence of a strong Sigma-m-plus-one nesting on beta, assuming L-beta satisfies V=HC.
References
If $L_\beta\models\mbox{$\mathit{V}=\mathit{HC}$}$, then
\left(\mathcal{P}(\omega)\cap L_\beta\models\bm{\Pi}{m+1}1\mathsf{-MI}\,\right)\iff\beta\mbox{ supports a strong }\Sigma{m+1}\textrm{-nesting}.
— Open Problems in Mathematical Logic
(2608.26628 - Barmpalias et al., 27 Aug 2026) in Section 10