{"title":"规则是II_2^0-微积分中很难","authors":"B. Intrigila, R. Statman","doi":"10.1109/LICS.2004.1319614","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2004-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Omega Rule is II_2^0-Hard in the lambda beta -Calculus\",\"authors\":\"B. Intrigila, R. Statman\",\"doi\":\"10.1109/LICS.2004.1319614\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":6322,\"journal\":{\"name\":\"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-07-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/LICS.2004.1319614\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.2004.1319614","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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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