  We show that neither the class of C*-algebras with Kirchberg's QWEP property
nor the class of W*-probability spaces with the QWEP property are effectively
axiomatizable (in the appropriate languages). The latter result follows from a
more general result, namely that the hyperfinite III$_1$ factor does not have a
computable universal theory in the language of W*-probability spaces. We also
prove that the Powers' factors $\mathcal{R}_\lambda$, for $0<\lambda<1$, when
equipped with their canonical Powers' states, do not have computable universal
theory.
