The omega rule is Π11-complete in the λβ-calculus

Authors:
Benedetto Intrigila;Richard Statman
Affiliations:
Università di Roma "Tor Vergata", Rome, Italy;Carnegie-Mellon University, Pittsburgh, PA
Venue:
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Year:
2007

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Abstract

We give a many-one reduction of the set of true Π11 sentences to the set of consequences of the λ-calculus with the ω-rule. This solves in the affirmative a long-standing problem of H. Barendregt (1975).