  If $A_n$ is a sequence of C*-algebras, then the C*-algebra $\prod A_n /
\bigoplus A_n$ is called a reduced product. We prove, assuming Todorcevic's
Axiom and Martin's Axiom, that every isomorphism between two reduced products
of separable, unital UHF algebras must be definable in a strong sense. As a
corollary we deduce that two such reduced products $\prod A_n / \bigoplus A_n$
and $\prod B_n / \bigoplus B_n$ are isomorphic if and only if, up to an
almost-permutation of $\mathbb{N}$, $A_n$ is isomorphic to $B_n$.
