4. Nuclearity

Problem 4.1.
Is every stably finite nuclear separable C*algebra locally approximable by type I C*algebras? 
All presently known nuclear C*algebras are obtained from $\mathbb C$ by taking closure under simple operations such as tensoring with finitedimensional matrix algebras and taking inductive limits. They belong to the socalled bootstrap class.
Problem 4.2.
Does every nuclear C*algebra belong to the bootstrap class?
Cite this as: AimPL: Set theory and C* algebras, available at http://aimpl.org/settheorycstar.