{"title":"Different covering numbers of compact tree ideals","authors":"Jelle Mathis Kuiper, Otmar Spinas","doi":"10.1007/s00153-024-00933-6","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate the covering numbers of some ideals on <span>\\({^{\\omega }}{2}{}\\)</span> associated with tree forcings. We prove that the covering of the Sacks ideal remains small in the Silver and uniform Sacks model, respectively, and that the coverings of the uniform Sacks ideal and the Mycielski ideal, <span>\\({\\mathfrak {C}_{2}}\\)</span>, remain small in the Sacks model.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"64 1-2","pages":"259 - 278"},"PeriodicalIF":0.3000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-024-00933-6.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00153-024-00933-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate the covering numbers of some ideals on \({^{\omega }}{2}{}\) associated with tree forcings. We prove that the covering of the Sacks ideal remains small in the Silver and uniform Sacks model, respectively, and that the coverings of the uniform Sacks ideal and the Mycielski ideal, \({\mathfrak {C}_{2}}\), remain small in the Sacks model.
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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