**Question 1.** What is known about the consistency strength of $\aleph_2$-Souslin hypothesis?

**Question 2.** What is known about the consistency strength of having both $\aleph_2$-Souslin hypotheis and $\aleph_3$-Souslin hypothesis?

**Remark 1.** By $\kappa$-Souslin hopothesis, I mean there are no $\kappa$-Souslin trees.

**Remark 2.** By Laver-Shelah, the existence of a weakly compact cardinal implies the consistency of $\aleph_2$-Souslin hypothesis. On the other hand by results of Shelah-Stanly, if we assume some instances of $GCH$+ $\aleph_2$-Souslin hypothesis (having $CH$ is sufficient), then some large cardinals (at least Mahlo) are required. In the above question I do not take care of preserving instances of $GCH$.