We say that a statement φ is Ω-satisfiable if there exists an ordinal α and a complete Boolean algebra B such that VBα ⊧ φ, and we say that φ is Ω-valid if ∅ ⊧Ω φ. So, the above theorem says that (under our background assumptions), the statement “φ is Ω-satisfiable” is generically invariant and in terms of Ω-validity this is simply the following: 