索洛维还原性意味着 S2a 还原性

arXiv - MATH - Logic Pub Date : 2024-08-07 DOI:arxiv-2408.04074

Ivan Titov

{"title":"索洛维还原性意味着 S2a 还原性","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original notion of Solovay reducibility was introduced by Robert M.\nSolovay (unpublished notes) in 1975 as a measure of relative randomness.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":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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original notion of Solovay reducibility was introduced by Robert M.\\nSolovay (unpublished notes) in 1975 as a measure of relative randomness.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\":null,\"pages\":null},\"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}","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

摘要

索洛维可还原性的最初概念是由罗伯特-索洛维（Robert M.Solovay）（未发表的笔记）于1975年提出的，作为一种相对随机性的度量。郑锡忠和罗伯特-雷廷格（DOI:10.1007/978-3-540-27798-9_39）于 2004 年提出的 S2a-reducibility 是对索洛维可简化性的修改，适用于可计算近似（c.a. ）的实数。我们证明了索洛维可简化性意味着 c.a. 复数集上的 S2a 可简化性，即使使用同一个常数也是如此，反之亦然。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Solovay reducibility implies S2a-reducibility

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Logic

自引率

0.00%

发文量