{"title":"关于不存在\\(\\kappa \\)疯狂家庭","authors":"Haim Horowitz, Saharon Shelah","doi":"10.1007/s00153-023-00874-6","DOIUrl":null,"url":null,"abstract":"<div><p>Starting from a model with a Laver-indestructible supercompact cardinal <span>\\(\\kappa \\)</span>, we construct a model of <span>\\(ZF+DC_{\\kappa }\\)</span> where there are no <span>\\(\\kappa \\)</span>-mad families.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00874-6.pdf","citationCount":"0","resultStr":"{\"title\":\"On the non-existence of \\\\(\\\\kappa \\\\)-mad families\",\"authors\":\"Haim Horowitz, Saharon Shelah\",\"doi\":\"10.1007/s00153-023-00874-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Starting from a model with a Laver-indestructible supercompact cardinal <span>\\\\(\\\\kappa \\\\)</span>, we construct a model of <span>\\\\(ZF+DC_{\\\\kappa }\\\\)</span> where there are no <span>\\\\(\\\\kappa \\\\)</span>-mad families.</p></div>\",\"PeriodicalId\":48853,\"journal\":{\"name\":\"Archive for Mathematical Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-05-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00153-023-00874-6.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive for Mathematical Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00153-023-00874-6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00153-023-00874-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
Starting from a model with a Laver-indestructible supercompact cardinal \(\kappa \), we construct a model of \(ZF+DC_{\kappa }\) where there are no \(\kappa \)-mad families.
期刊介绍：
The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.
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