Unsolved Problems

If $\kappa$ is a singular strong limit cardinal, then $2^\kappa = \kappa^+$....

Is every abelian group $A$ such that $\text{Ext}^1(A, \mathbb{Z}) = 0$ a free abelian group?...

Does the partition principle (PP) imply the axiom of choice (AC)?...

Does the generalized continuum hypothesis imply the existence of an $\aleph_2$-Suslin tree?...

Does there exist a Jónsson algebra on $\aleph_\omega$?...

Is the open coloring axiom (OCA) consistent with $2^{\aleph_0} > \aleph_2$?...