超紧性可以与可测性相等

IF 0.6 3区数学 Q2 LOGIC

Notre Dame Journal of Formal Logic Pub Date : 2021-11-01 DOI:10.1215/00294527-2021-0031

Nam Trang

{"title":"超紧性可以与可测性相等","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":"{\"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}","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

摘要

本文在文献[19]和文献[16]的基础上，证明了“ADR + DC +在Θ上有一个R完备测度”与“ZF + DC + ADR +在p ω1(p (R)) + Θ上有一个超紧测度”是等价的。这里提出的结果和技术有助于描述内模型理论的一般程序，特别是对ZF + DC背景下紧性现象的一般研究。

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

Supercompactness Can Be Equiconsistent with Measurability

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.

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

Notre Dame Journal of Formal Logic MATHEMATICS-LOGIC

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

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.