4 problems

Failure-of-square equiconsistency conjecture. The following theories are equiconsistent:

Steel's conjecture. The failure of … boxvoidkappa $$ is at least as strong as the existence of a superstrong cardinal.

Let $\Theta^\infty=\Theta^{L(\Gamma^\infty,\mathbb{R})}$ and let $L(\mathcal{A}^\infty)$ be the model generated by $\mathcal{A}^\infty$. Square-sequence conjecture. … The claim is…

Let $M eprec Htheta$ be a guessing model and let $lambdain M$ be a regular cardinal above $kappaM$. Boundedness conjecture. One has … This would remove the boundedness assumption f…