{"title":"无根魏氏度","authors":"Patrick Uftring","doi":"10.3233/com-230471","DOIUrl":null,"url":null,"abstract":"We answer the following question by Arno Pauly: “Is there a square root operator on the Weihrauch degrees?”. In fact, we show that there are uncountably many pairwise incomparable Weihrauch degrees without any roots. We also prove that the omniscience principles of LPO and LLPO do not have roots.","PeriodicalId":515920,"journal":{"name":"Computability","volume":"83 8","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weihrauch degrees without roots\",\"authors\":\"Patrick Uftring\",\"doi\":\"10.3233/com-230471\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We answer the following question by Arno Pauly: “Is there a square root operator on the Weihrauch degrees?”. In fact, we show that there are uncountably many pairwise incomparable Weihrauch degrees without any roots. We also prove that the omniscience principles of LPO and LLPO do not have roots.\",\"PeriodicalId\":515920,\"journal\":{\"name\":\"Computability\",\"volume\":\"83 8\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3233/com-230471\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3233/com-230471","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We answer the following question by Arno Pauly: “Is there a square root operator on the Weihrauch degrees?”. In fact, we show that there are uncountably many pairwise incomparable Weihrauch degrees without any roots. We also prove that the omniscience principles of LPO and LLPO do not have roots.
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