We extend the classical Feferman–Vaught theorem to logic for metric structures. This implies that the reduced powers of elementarily equivalent structures are elementarily equivalent, and therefore they are isomorphic under the Continuum Hypothesis. We also prove the existence of two separable C*-algebras of the form ⊕iMk(i) (ℂ) such that the assertion that their coronas are isomorphic is independent from ZFC, which gives the first example of genuinely noncommutative coronas of separable C*-algebras with this property.
