合度和柱体

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Journal of Logic and Computation Pub Date : 2023-10-25 DOI:10.1093/logcom/exad064

Irakli Chitaia, Roland Omanadze, Andrea Sorbi

{"title":"合度和柱体","authors":"Irakli Chitaia, Roland Omanadze, Andrea Sorbi","doi":"10.1093/logcom/exad064","DOIUrl":null,"url":null,"abstract":"Abstract In this article, we define and study the notion of a $(c,c_{1})$-cylinder, which turns out to be very useful instrument for investigating the relationships between conjunctive reducibility ($c$-reducibility) and its injective version $c_{1}$-reducibility. Using this notion, we prove the following results: (i) Neither hypersimple sets nor hemimaximal sets can be $(c,c_{1})$-cylinders; (ii) The $c$-degree of a noncomputable c.e. set contains either only one or infinitely many noncomputable $c_{1}$-degrees; (iii) the $c$-degree of either a hemimaximal set or a hypersimple set contains infinitely many noncomputable $c_{1}$-degrees.","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":"72 2","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Conjunctive degrees and cylinders\",\"authors\":\"Irakli Chitaia, Roland Omanadze, Andrea Sorbi\",\"doi\":\"10.1093/logcom/exad064\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this article, we define and study the notion of a $(c,c_{1})$-cylinder, which turns out to be very useful instrument for investigating the relationships between conjunctive reducibility ($c$-reducibility) and its injective version $c_{1}$-reducibility. Using this notion, we prove the following results: (i) Neither hypersimple sets nor hemimaximal sets can be $(c,c_{1})$-cylinders; (ii) The $c$-degree of a noncomputable c.e. set contains either only one or infinitely many noncomputable $c_{1}$-degrees; (iii) the $c$-degree of either a hemimaximal set or a hypersimple set contains infinitely many noncomputable $c_{1}$-degrees.\",\"PeriodicalId\":50162,\"journal\":{\"name\":\"Journal of Logic and Computation\",\"volume\":\"72 2\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Logic and Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/logcom/exad064\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logic and Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/logcom/exad064","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文定义并研究了$(c,c_{1})$-柱体的概念，它是研究合约可约性($c$-可约性)与其内射版本$c_{1}$-可约性之间关系的一个非常有用的工具。利用这一概念，我们证明了以下结果:(i)超简单集和半极大集都不能是$(c,c_{1})$-柱体;(ii)不可计算的c.e.集的$c$-度只包含一个或无限多个不可计算的$c_{1}$-度;(iii)半极大集或超简单集的$c$-度包含无限多个不可计算的$c_{1}$-度。

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

Conjunctive degrees and cylinders

Abstract In this article, we define and study the notion of a $(c,c_{1})$-cylinder, which turns out to be very useful instrument for investigating the relationships between conjunctive reducibility ($c$-reducibility) and its injective version $c_{1}$-reducibility. Using this notion, we prove the following results: (i) Neither hypersimple sets nor hemimaximal sets can be $(c,c_{1})$-cylinders; (ii) The $c$-degree of a noncomputable c.e. set contains either only one or infinitely many noncomputable $c_{1}$-degrees; (iii) the $c$-degree of either a hemimaximal set or a hypersimple set contains infinitely many noncomputable $c_{1}$-degrees.

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

Journal of Logic and Computation 工程技术-计算机：理论方法

CiteScore

1.90

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Logic has found application in virtually all aspects of Information Technology, from software engineering and hardware to programming and artificial intelligence. Indeed, logic, artificial intelligence and theoretical computing are influencing each other to the extent that a new interdisciplinary area of Logic and Computation is emerging. The Journal of Logic and Computation aims to promote the growth of logic and computing, including, among others, the following areas of interest: Logical Systems, such as classical and non-classical logic, constructive logic, categorical logic, modal logic, type theory, feasible maths.... Logical issues in logic programming, knowledge-based systems and automated reasoning; logical issues in knowledge representation, such as non-monotonic reasoning and systems of knowledge and belief; logics and semantics of programming; specification and verification of programs and systems; applications of logic in hardware and VLSI, natural language, concurrent computation, planning, and databases. The bulk of the content is technical scientific papers, although letters, reviews, and discussions, as well as relevant conference reviews, are included.