许多强制公理适用于所有正则不可数基数

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics Pub Date : 2023-11-13 DOI:10.1007/s11856-023-2570-0

Noam Greenberg, Saharon Shelah

{"title":"许多强制公理适用于所有正则不可数基数","authors":"Noam Greenberg, Saharon Shelah","doi":"10.1007/s11856-023-2570-0","DOIUrl":null,"url":null,"abstract":"Abstract A central theme in set theory is to find universes with extreme, well-understood behaviour. The case we are interested in is assuming GCH and having a strong forcing axiom of higher order than usual. Instead of “every suitable forcing notion of size λ has a sufficiently generic filter” we shall say “for every suitable method of producing notions of forcing based on a given stationary set, there is such a suitable stationary set S and sufficiently generic filters for the notion of forcing attached to S ”. Such notions of forcing are important for Abelian group theory, but this application is delayed for a sequel.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Many forcing axioms for all regular uncountable cardinals\",\"authors\":\"Noam Greenberg, Saharon Shelah\",\"doi\":\"10.1007/s11856-023-2570-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract A central theme in set theory is to find universes with extreme, well-understood behaviour. The case we are interested in is assuming GCH and having a strong forcing axiom of higher order than usual. Instead of “every suitable forcing notion of size λ has a sufficiently generic filter” we shall say “for every suitable method of producing notions of forcing based on a given stationary set, there is such a suitable stationary set S and sufficiently generic filters for the notion of forcing attached to S ”. Such notions of forcing are important for Abelian group theory, but this application is delayed for a sequel.\",\"PeriodicalId\":14661,\"journal\":{\"name\":\"Israel Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Israel Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11856-023-2570-0\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Israel Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11856-023-2570-0","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

集合论的一个中心主题是寻找具有极端、可理解行为的宇宙。我们感兴趣的情况是假设GCH并且有一个强强迫公理比通常的高阶。而不是“每一个大小为λ的合适的强迫概念都有一个足够一般的过滤器”，我们应该说“对于每一个基于给定平稳集产生强迫概念的合适方法，都有这样一个合适的平稳集S和附在S上的强迫概念的足够一般过滤器”。这种强迫的概念对于阿贝尔群论是很重要的，但是这个应用被推迟到后续。

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

Many forcing axioms for all regular uncountable cardinals

Abstract A central theme in set theory is to find universes with extreme, well-understood behaviour. The case we are interested in is assuming GCH and having a strong forcing axiom of higher order than usual. Instead of “every suitable forcing notion of size λ has a sufficiently generic filter” we shall say “for every suitable method of producing notions of forcing based on a given stationary set, there is such a suitable stationary set S and sufficiently generic filters for the notion of forcing attached to S ”. Such notions of forcing are important for Abelian group theory, but this application is delayed for a sequel.

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

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.