{"title":"A continuum of theories of lambda calculus without semantics","authors":"A. Salibra","doi":"10.1109/LICS.2001.932509","DOIUrl":null,"url":null,"abstract":"In this paper, we give a topological proof of the following result: there exist 2¿(/spl aleph//sub 0/) lambda theories of the untyped lambda calculus without a model in any semantics based on D.S. Scott's (1972, 1981) view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this result, we positively solve the conjecture, stated by O. Bastonero and X. Gouy (1999) and by C. Berline (2000), that the strongly stable semantics is incomplete.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"279 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"22","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.2001.932509","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 22
Abstract
In this paper, we give a topological proof of the following result: there exist 2¿(/spl aleph//sub 0/) lambda theories of the untyped lambda calculus without a model in any semantics based on D.S. Scott's (1972, 1981) view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this result, we positively solve the conjecture, stated by O. Bastonero and X. Gouy (1999) and by C. Berline (2000), that the strongly stable semantics is incomplete.
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