Robinson forcing and the quasidiagonality problem

Abstract

We introduce weakenings of two of the more prominent open problems in the classification of ${\mathrm{C}}^{\ast }$-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 ${\mathrm{C}}^{\ast }$-algebra is MF.

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