  We introduce weakenings of two of the more prominent open problems in the
classification of $\mathrm{C}^*$-algebras, namely the quasidiagonality problem
and the UCT problem. We show that the a positive solution of the conjunction of
the two weaker problems implies a positive solution of the original
quasidiagonality problem as well as allows us to give a local, finitary
criteria for the MF problem, which asks whether every stably finite
$\mathrm{C}^*$-algebra is MF.
