## Paper: The Omega Rule is II_2^0-Hard in the λβ-Calculus (at LICS 2004)

**Benedetto Intrigila Richard Statman**

### Abstract

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.

### BibTeX

@InProceedings{IntrigilaStatman-TheOmegaRuleisII20H, author = {Benedetto Intrigila and Richard Statman}, title = {The Omega Rule is II_2^0-Hard in the λβ-Calculus}, booktitle = {Proceedings of the Nineteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2004)}, year = {2004}, month = {July}, pages = {202--210}, location = {Turku, Finland}, publisher = {IEEE Computer Society Press} }