{"title":"Esakia 定理在一元环境中的失败","authors":"Guram Bezhanishvili, Luca Carai","doi":"arxiv-2409.05607","DOIUrl":null,"url":null,"abstract":"Esakia's theorem states that Grzegorczyk's logic is the largest modal\ncompanion of intuitionistic propositional calculus. We prove that already the\none-variable fragment of intuitionistic predicate calculus does not have the\nlargest modal companion, yielding that Esakia's theorem fails in the monadic\nsetting.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Failure of Esakia's theorem in the monadic setting\",\"authors\":\"Guram Bezhanishvili, Luca Carai\",\"doi\":\"arxiv-2409.05607\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Esakia's theorem states that Grzegorczyk's logic is the largest modal\\ncompanion of intuitionistic propositional calculus. We prove that already the\\none-variable fragment of intuitionistic predicate calculus does not have the\\nlargest modal companion, yielding that Esakia's theorem fails in the monadic\\nsetting.\",\"PeriodicalId\":501306,\"journal\":{\"name\":\"arXiv - MATH - Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.05607\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05607","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Failure of Esakia's theorem in the monadic setting
Esakia's theorem states that Grzegorczyk's logic is the largest modal
companion of intuitionistic propositional calculus. We prove that already the
one-variable fragment of intuitionistic predicate calculus does not have the
largest modal companion, yielding that Esakia's theorem fails in the monadic
setting.
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