The Omega Rule is II_2^0-Hard in the β-Calculus
Benedetto Intrigila, Richard Statman · Logic in Computer Science · 2004
We give a many-one reduction of the set of true II_2^0 sentences to the set of consequences of the lambda calculus with the omega rule.This solves in the affirmative a well known problem of H.Barendregt.The technique of proof has interest in itself and can be extended to prove that the theory which identifies all unsolvable terms together with the omega rule is II_1^1-complete which solves another long-standing conjecture of H. Barendregt.