CH equivalence of isomorphism between unstable reduced products over Fin and ultrapowers

Determine whether the assertion that a nontrivial reduced product ∏_n M_n/Fin with unstable first-order theory is isomorphic to a nontrivial ultrapower associated with a nonprincipal ultrafilter on N is equivalent to the Continuum Hypothesis (CH).

Background

The authors prove there is a forcing extension in which every reduced product over Fin with unstable theory is not isomorphic to any ultrapower. Under CH, many classical isomorphism and saturation phenomena align ultraproducts and reduced products.

They explicitly note that it is unknown whether the isomorphism assertion is equivalent to CH, pointing to a question in earlier work. Resolving this would clarify the exact role of CH in determining when unstable reduced products can be represented as ultrapowers.