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FACTORIALS OF INFINITE CARDINALS IN ZF PART I: ZF RESULTS

文献类型：期刊论文

作者Shen, Guozhen1,2; Yuan, Jiachen3,4
刊名JOURNAL OF SYMBOLIC LOGIC
出版日期2020-03-01
卷号85期号:1页码:224-243
关键词ZF cardinal factorial permutation finite-to-one function Dedekind finite
ISSN号0022-4812
DOI10.1017/jsl.2019.74
英文摘要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.
资助项目NSFC[11871464]
WOS研究方向Mathematics ; Science & Technology - Other Topics
语种英语
WOS记录号WOS:000525578300011
出版者CAMBRIDGE UNIV PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/51205]  
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, LPMC, Tianjin 300071, Peoples R China
4.Nankai Univ, Sch Math Sci, 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.

入库方式： OAI收割

来源：数学与系统科学研究院

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