{"title":"Ershov层次超限层中的弱密度和非密度","authors":"Yong Liu, Cheng Peng","doi":"10.1215/00294527-2020-0023","DOIUrl":null,"url":null,"abstract":"We show that for any ω-r.e. degree d and n-r.e. degree b with d<b, there is an (ω+1)-r.e. degree a strictly between d and b. We also show that there is a maximal incomplete (ω+1)-r.e. degree. As a corollary, Dω is not a Σ1-elementary substructure of Dω+1.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Weak Density and Nondensity among Transfinite Levels of the Ershov Hierarchy\",\"authors\":\"Yong Liu, Cheng Peng\",\"doi\":\"10.1215/00294527-2020-0023\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that for any ω-r.e. degree d and n-r.e. degree b with d<b, there is an (ω+1)-r.e. degree a strictly between d and b. We also show that there is a maximal incomplete (ω+1)-r.e. degree. As a corollary, Dω is not a Σ1-elementary substructure of Dω+1.\",\"PeriodicalId\":51259,\"journal\":{\"name\":\"Notre Dame Journal of Formal Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Notre Dame Journal of Formal Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1215/00294527-2020-0023\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Notre Dame Journal of Formal Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/00294527-2020-0023","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
期刊介绍:
The Notre Dame Journal of Formal Logic, founded in 1960, aims to publish high quality and original research papers in philosophical logic, mathematical logic, and related areas, including papers of compelling historical interest. The Journal is also willing to selectively publish expository articles on important current topics of interest as well as book reviews.