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The omega rule is Π20-hard in the λβ-calculus

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2 Author(s)
B. Intrigila ; Univ. degli Studi di L'Aquila, Italy ; R. Statman

We give a many-one reduction of the set of true Π20 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 H11-complete which solves another long-standing conjecture of H. Barendregt.

Published in:

Logic in Computer Science, 2004. Proceedings of the 19th Annual IEEE Symposium on

Date of Conference:

13-17 July 2004