FACTORIALS OF INFINITE CARDINALS IN ZF PART II: CONSISTENCY RESULTS

doi:10.1017/jsl.2019.75

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	FACTORIALS OF INFINITE CARDINALS IN ZF PART II: CONSISTENCY 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:244-270
摘要	For a set x, let S(x) be the set of all permutations of x. We prove by the method of permutation models that the following statements are consistent with ZF: (1) There is an infinite set x such that vertical bar p(x)vertical bar < vertical bar S(x)vertical bar < vertical bar seq(1-1)(x)vertical bar < vertical bar seq(x)vertical bar, where p(x) is the power set of x, seq(x) is the set of all finite sequences of elements of x, and seq(1)-(1()x) is the set of all finite sequences of elements of x without repetition. (2) There is a Dedekind infinite set x such that vertical bar S(x)vertical bar < vertical bar[x](3)vertical bar and such that there exists a surjection from x onto S(x). (3) There is an infinite set x such that there is a finite-to-one function from S(x) into x.
关键词	ZF cardinal factorial permutation permutation model finite-to-one function
DOI	10.1017/jsl.2019.75
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:000525578300012
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/51086
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 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 II: CONSISTENCY RESULTS[J]. JOURNAL OF SYMBOLIC LOGIC,2020,85(1):244-270.
APA	Shen, Guozhen,&Yuan, Jiachen.(2020).FACTORIALS OF INFINITE CARDINALS IN ZF PART II: CONSISTENCY RESULTS.JOURNAL OF SYMBOLIC LOGIC,85(1),244-270.
MLA	Shen, Guozhen,et al."FACTORIALS OF INFINITE CARDINALS IN ZF PART II: CONSISTENCY RESULTS".JOURNAL OF SYMBOLIC LOGIC 85.1(2020):244-270.