FACTORIALS OF INFINITE CARDINALS IN ZF PART II: CONSISTENCY RESULTS
文献类型：期刊论文
| 作者 | Shen, Guozhen3,4; Yuan, Jiachen1,2 |
| 刊名 | JOURNAL OF SYMBOLIC LOGIC
 |
| 出版日期 | 2020-03-01 |
| 卷号 | 85期号:1页码:244-270 |
| 关键词 | ZF cardinal factorial permutation permutation model finite-to-one function |
| ISSN号 | 0022-4812 |
| DOI | 10.1017/jsl.2019.75 |
| 英文摘要 | 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. |
| 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:000525578300012 |
| 出版者 | CAMBRIDGE UNIV PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51085]  |
| 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.Nankai Univ, LPMC, Tianjin 300071, Peoples R China 2.Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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