Shoenfield's Absoluteness Theorem

Shoenfield's Absoluteness Theorem, proved by Joseph Shoenfield in 1961, states that every Sigma-1-2 and Pi-1-2 statement of the analytical hierarchy has the same truth value in any transitive model of set theory and in that model's own constructible universe, provided both contain the same ordinals. The theorem shows that a wide class of statements, including most classical questions of analysis and descriptive set theory, cannot be shown independent of the standard ZFC axioms by the method of forcing, since a forcing extension and its ground model must agree on every statement in this class.