关于分裂井集

IF 0.3 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2022-03-09 DOI:10.1007/s00153-022-00818-6

Dušan Repovš, Lyubomyr Zdomskyy

{"title":"关于分裂井集","authors":"Dušan Repovš, Lyubomyr Zdomskyy","doi":"10.1007/s00153-022-00818-6","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce a class of proper posets which is preserved under countable support iterations, includes <span>\\(\\omega ^\\omega \\)</span>-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the property that the ground model reals remain splitting and unbounded in corresponding extensions. Our results may be considered as a possible path towards solving variations of the famous Roitman problem.\n</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On well-splitting posets\",\"authors\":\"Dušan Repovš, Lyubomyr Zdomskyy\",\"doi\":\"10.1007/s00153-022-00818-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce a class of proper posets which is preserved under countable support iterations, includes <span>\\\\(\\\\omega ^\\\\omega \\\\)</span>-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the property that the ground model reals remain splitting and unbounded in corresponding extensions. Our results may be considered as a possible path towards solving variations of the famous Roitman problem.\\n</p></div>\",\"PeriodicalId\":48853,\"journal\":{\"name\":\"Archive for Mathematical Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-03-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive for Mathematical Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00153-022-00818-6\",\"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/s00153-022-00818-6","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: 1

摘要

我们引入了一类在可数支持迭代下保持的固有偏序集，包括\(\omega ^\omega \) -bounding、Cohen、Miller和Mathias偏序集，这些偏序集与具有Hurewicz覆盖性质的滤波器相关联，并且在相应的扩展中具有地面模型实数保持分裂和无界的性质。我们的结果可能被认为是解决著名的Roitman问题的一个可能的途径。

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

On well-splitting posets

We introduce a class of proper posets which is preserved under countable support iterations, includes \(\omega ^\omega \)-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the property that the ground model reals remain splitting and unbounded in corresponding extensions. Our results may be considered as a possible path towards solving variations of the famous Roitman problem.

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

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

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.