SCHEEPERS' CONJECTURE AND THE SCHEEPERS DIAGRAM
文献类型：期刊论文
| 作者 | Peng, Yinhe |
| 刊名 | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
 |
| 出版日期 | 2022-11-16 |
| 页码 | 31 |
| 关键词 | Subject Classification Selection principles Scheepers? conjecture Scheepers diagram almost finite |
| ISSN号 | 0002-9947 |
| DOI | 10.1090/tran/8787 |
| 英文摘要 | Inductively approaching subsets by almost finite sets, we refute Scheepers' conjecture under CH. More precisely, we prove the following. (1) Assuming CH, there is a subset of reals X such that Cp(X) has property (alpha 2) and X does not satisfy S1(Gamma, Gamma). Applying the idea of approaching subsets by almost finite sets and using an analogous approaching, we complete the Scheepers Diagram. (2) Ufin(Gamma,Gamma) implies Sfin(Gamma, S2). (3) Ufin(Gamma, S2) does not imply Sfin(Gamma, S2). More precisely, assuming CH, there is a subset of reals X satisfying Ufin(Gamma, S2) such that X does not satisfy Sfin(Gamma, S2). These results solve three longstanding and major problems in selection principles. |
| 资助项目 | NSFC[11901562] ; Chinese Academy of Sciences |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000886291000001 |
| 出版者 | AMER MATHEMATICAL SOC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60622]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Peng, Yinhe |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, East Zhong Guan Cun Rd 55, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Peng, Yinhe. SCHEEPERS' CONJECTURE AND THE SCHEEPERS DIAGRAM[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2022:31. |
| APA | Peng, Yinhe.(2022).SCHEEPERS' CONJECTURE AND THE SCHEEPERS DIAGRAM.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,31. |
| MLA | Peng, Yinhe."SCHEEPERS' CONJECTURE AND THE SCHEEPERS DIAGRAM".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2022):31. |
入库方式： OAI收割
来源：数学与系统科学研究院
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