SCHEEPERS' CONJECTURE AND THE SCHEEPERS DIAGRAM

doi:10.1090/tran/8787

	SCHEEPERS' CONJECTURE AND THE SCHEEPERS DIAGRAM
	Peng, Yinhe
刊名	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
	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
出版者	AMER MATHEMATICAL SOC
WOS记录号	WOS:000886291000001
内容类型	期刊论文
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.