FACTORIALS OF INFINITE CARDINALS IN ZF PART I: ZF RESULTS

doi:10.1017/jsl.2019.74

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	FACTORIALS OF INFINITE CARDINALS IN ZF PART I: ZF RESULTS
	Shen, Guozhen 1,2; Yuan, Jiachen 3,4
	2020-03-01
发表期刊	JOURNAL OF SYMBOLIC LOGIC
ISSN	0022-4812
卷号	85 期号:1 页码:224-243
摘要	For a set x, let S(x) be the set of all permutations of x. We prove in ZF (without the axiom of choice) several results concerning this notion, among which are the following: (1) For all sets x such that S(x) is Dedekind infinite, vertical bar S-fin(x)vertical bar < vertical bar S(x)vertical bar and there are no finite-to-one functions from S(x) into S-fin(x), where S-fin(x) denotes the set of all permutations of x which move only finitely many elements. (2) For all sets x such that S(x) isDedekind infinite, vertical bar seq(x)vertical bar < vertical bar S(x)vertical bar and there are no finite-to-one functions from S(x) into seq(x), where seq(x) denotes the set of all finite sequences of elements of x. (3) For all infinite sets x such that there exists a permutation of x without fixed points, there are no finite-to-one functions from S(x) into x. (4) For all sets x, vertical bar[x](2)vertical bar < vertical bar S(x)vertical bar.
关键词	ZF cardinal factorial permutation finite-to-one function Dedekind finite
DOI	10.1017/jsl.2019.74
收录类别	SCI
语种	英语
资助项目	NSFC[11871464]
WOS研究方向	Mathematics ; Science & Technology - Other Topics
WOS类目	Mathematics ; Logic
WOS记录号	WOS:000525578300011
出版者	CAMBRIDGE 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/51206
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, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China 4.Nankai Univ, LPMC, Tianjin 300071, Peoples R China
推荐引用方式 GB/T 7714	Shen, Guozhen,Yuan, Jiachen. FACTORIALS OF INFINITE CARDINALS IN ZF PART I: ZF RESULTS[J]. JOURNAL OF SYMBOLIC LOGIC,2020,85(1):224-243.
APA	Shen, Guozhen,&Yuan, Jiachen.(2020).FACTORIALS OF INFINITE CARDINALS IN ZF PART I: ZF RESULTS.JOURNAL OF SYMBOLIC LOGIC,85(1),224-243.
MLA	Shen, Guozhen,et al."FACTORIALS OF INFINITE CARDINALS IN ZF PART I: ZF RESULTS".JOURNAL OF SYMBOLIC LOGIC 85.1(2020):224-243.