  We consider isomorphisms between quotient algebras of $\prod_{n=0}^{\infty}
\mathbb{M}_{k(n)}(\mathbb{C})$ associated with Borel ideals on $\mathbb{N}$ and
prove that it is relatively consistent with \textbf{ZFC} that all of these
isomorphisms are trivial, in the sense that they lift to a *-homomorphism from
$\prod_{n=0}^{\infty} \mathbb{M}_{k(n)}(\mathbb{C})$ into itself. This
generalizes a result of Farah-Shelah who proved this result for centers of
these algebras (in its dual form). We also use a simpler forcing notion and
completely remove the large cardinal assumption used by Farah-Shelah.
