A Note on Strongly Almost Disjoint Families

doi:10.1215/00294527-2020-0002

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	A Note on Strongly Almost Disjoint Families
	Shen, Guozhen 1,2
	2020-05-01
发表期刊	NOTRE DAME JOURNAL OF FORMAL LOGIC
ISSN	0029-4527
卷号	61 期号:2 页码:227-231
摘要	For a set M, let vertical bar M vertical bar denote the cardinality of M. A family F is called strongly almost disjoint if there is an n is an element of omega such that vertical bar A boolean AND B < n for any two distinct elements A, B of F. It is shown in ZF (without the axiom of choice) that, for all infinite sets M and all strongly almost disjoint families F subset of P(M), vertical bar F vertical bar < vertical bar P(M)vertical bar and there are no finite-to-one functions from P(M) into F, where P(M) denotes the power set of M.
关键词	strongly almost disjoint family cardinality finite-to-one function axiom of choice
DOI	10.1215/00294527-2020-0002
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11871464]
WOS研究方向	Mathematics ; Science & Technology - Other Topics ; Philosophy
WOS类目	Mathematics ; Logic ; Philosophy
WOS记录号	WOS:000530106300003
出版者	DUKE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51388
专题	中国科学院数学与系统科学研究院
通讯作者	Shen, Guozhen
作者单位	1.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Shen, Guozhen. A Note on Strongly Almost Disjoint Families[J]. NOTRE DAME JOURNAL OF FORMAL LOGIC,2020,61(2):227-231.
APA	Shen, Guozhen.(2020).A Note on Strongly Almost Disjoint Families.NOTRE DAME JOURNAL OF FORMAL LOGIC,61(2),227-231.
MLA	Shen, Guozhen."A Note on Strongly Almost Disjoint Families".NOTRE DAME JOURNAL OF FORMAL LOGIC 61.2(2020):227-231.