{"title":"Martin's conjecture for regressive functions on the hyperarithmetic degrees","authors":"P. Lutz","doi":"10.1142/s0219061324500156","DOIUrl":null,"url":null,"abstract":"We answer a question of Slaman and Steel by showing that a version of Martin’s conjecture holds for all regressive functions on the hyperarithmetic degrees. A key step in our proof, which may have applications to other cases of Martin’s conjecture, consists of showing that we can always reduce to the case of a continuous function.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219061324500156","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 1
Abstract
We answer a question of Slaman and Steel by showing that a version of Martin’s conjecture holds for all regressive functions on the hyperarithmetic degrees. A key step in our proof, which may have applications to other cases of Martin’s conjecture, consists of showing that we can always reduce to the case of a continuous function.
期刊介绍:
The Journal of Mathematical Logic (JML) provides an important forum for the communication of original contributions in all areas of mathematical logic and its applications. It aims at publishing papers at the highest level of mathematical creativity and sophistication. JML intends to represent the most important and innovative developments in the subject.