{"title":"Solovay reducibility implies S2a-reducibility","authors":"Ivan Titov","doi":"arxiv-2408.04074","DOIUrl":null,"url":null,"abstract":"The original notion of Solovay reducibility was introduced by Robert M.\nSolovay (unpublished notes) in 1975 as a measure of relative randomness. The S2a-reducibility introduced by Xizhong Zheng and Robert Rettinger\n(DOI:10.1007/978-3-540-27798-9_39) in 2004 is a modification of Solovay\nreducibility suitable for computably approximable (c.a.) reals. We demonstrate that Solovay reducibility implies S2a-reducibility on the set\nof c.a. reals, even with the same constant, but not vice versa.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":"33 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-07","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-2408.04074","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The original notion of Solovay reducibility was introduced by Robert M.
Solovay (unpublished notes) in 1975 as a measure of relative randomness. The S2a-reducibility introduced by Xizhong Zheng and Robert Rettinger
(DOI:10.1007/978-3-540-27798-9_39) in 2004 is a modification of Solovay
reducibility suitable for computably approximable (c.a.) reals. We demonstrate that Solovay reducibility implies S2a-reducibility on the set
of c.a. reals, even with the same constant, but not vice versa.
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