{"title":"Supercompactness Can Be Equiconsistent with Measurability","authors":"Nam Trang","doi":"10.1215/00294527-2021-0031","DOIUrl":null,"url":null,"abstract":"The main result of this paper, built on work of [19] and [16], is the proof that the theory “ADR + DC + there is an R-complete measure on Θ” is equiconsistent with “ZF + DC + ADR + there is a supercompact measure on ℘ω1(℘(R)) + Θ is regular.” The result and techniques presented here contribute to the general program of descriptive inner model theory and in particular, to the general study of compactness phenomena in the context of ZF + DC.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":"18 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Notre Dame Journal of Formal Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/00294527-2021-0031","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 3
Abstract
The main result of this paper, built on work of [19] and [16], is the proof that the theory “ADR + DC + there is an R-complete measure on Θ” is equiconsistent with “ZF + DC + ADR + there is a supercompact measure on ℘ω1(℘(R)) + Θ is regular.” The result and techniques presented here contribute to the general program of descriptive inner model theory and in particular, to the general study of compactness phenomena in the context of ZF + DC.
期刊介绍：
The Notre Dame Journal of Formal Logic, founded in 1960, aims to publish high quality and original research papers in philosophical logic, mathematical logic, and related areas, including papers of compelling historical interest. The Journal is also willing to selectively publish expository articles on important current topics of interest as well as book reviews.
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