规则是II_2^0-微积分中很难

[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science Pub Date : 2004-07-13 DOI:10.1109/LICS.2004.1319614

B. Intrigila, R. Statman

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引用次数: 1

摘要

我们将true /spl Pi// sub2 //sup 0/句集简化为具有规则的λ演算结果集。这就肯定地解决了巴伦支的一个众所周知的问题。证明技术本身就很有趣，并且可以推广到证明与ω规则一起识别所有不可解项的理论是H/sub 1//sup 1/-完备的，这解决了H. Barendregt的另一个长期猜想。

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The Omega Rule is II_2^0-Hard in the lambda beta -Calculus

We give a many-one reduction of the set of true /spl Pi//sub 2//sup 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 H/sub 1//sup 1/-complete which solves another long-standing conjecture of H. Barendregt.

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[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science

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