4 problems

Let $A$ and $B$ be separable C-algebras, and let $\mathcal Q(A)$ and $\mathcal Q(B)$ denote their coronas. An isomorphism between these coronas is algebraically trivial if it arise…

The condensed Whitehead conjecture. Suppose that $A$ is an abelian group, $\mathbb{B}$ is a complete Boolean algebra, and

Proper destruction conjecture for MAD families. Every MAD family can be destroyed by a proper forcing that does not add dominating or unsplit reals.

Baumgartner's conjecture. Every forcing satisfying Axiom A can be embedded into an iteration of a $c\bf\sigmae$-closed forcing followed by a ccc forcing.