{"title":"可计算可枚举度的层次结构2","authors":"R. Downey, Noam Greenberg, Ellen Hammatt","doi":"10.53733/133","DOIUrl":null,"url":null,"abstract":"A transfinite hierarchy of Turing degrees of c.e.\\ sets has been used to calibrate the dynamics of families of constructions in computability theory, and yields natural definability results. We review the main results of the area, and discuss splittings of c.e.\\ degrees, and finding maximal degrees in upper cones.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"41 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hierarchy of Computably Enumerable Degrees II\",\"authors\":\"R. Downey, Noam Greenberg, Ellen Hammatt\",\"doi\":\"10.53733/133\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A transfinite hierarchy of Turing degrees of c.e.\\\\ sets has been used to calibrate the dynamics of families of constructions in computability theory, and yields natural definability results. We review the main results of the area, and discuss splittings of c.e.\\\\ degrees, and finding maximal degrees in upper cones.\",\"PeriodicalId\":30137,\"journal\":{\"name\":\"New Zealand Journal of Mathematics\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"New Zealand Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.53733/133\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"New Zealand Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.53733/133","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
A transfinite hierarchy of Turing degrees of c.e.\ sets has been used to calibrate the dynamics of families of constructions in computability theory, and yields natural definability results. We review the main results of the area, and discuss splittings of c.e.\ degrees, and finding maximal degrees in upper cones.
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