| 张东摩,肖奚安.经典公理集合论系统与中介公理集合论系统之间的包含关系[J].数学研究及应用,1997,17(3):475~478 |
| 经典公理集合论系统与中介公理集合论系统之间的包含关系 |
| Inclusion Relationship between Classical Axiomatic Set Theory and Madium Axiomatic Set Theory |
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| DOI：10.3770/j.issn:1000-341X.1997.03.030 |
| 中文关键词: 公理集合论 中介公理集合论 |
| 英文关键词:axiomatic set theory medium axiomatic set theory. |
| 基金项目:国家高技术863计划资助. |
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| 中文摘要: |
| 本文首先在中介公理集合论系统ＭＳ中构造出Ｐｅａｎｏ自然数系统，以此为基础重新定义了ＭＳ中的良集概念，证明了新定义的良集满足经典公理集合论系统ＺＦＣ－（ＺＦＣ中去掉正则公理的集合论系统）的全部公理，从而说明经典公理集合论系统ＺＦＣ－为中介公理集合论系统ＭＳ的子系统． |
| 英文摘要: |
| In this paper, Peano′s natural number system is constructed in the medium axiomatic set theory (MS). Based on this construction, the definition of well set in MS is redefined, and it is proved that redefined well set satisfies all the axioms of axiomatic set theory system ZFC－(a subsystem of ZFC without the regular axiom). It is concluded, therefore, that the classical axiomatic set theory system ZFC－ is a subsystem of the medium axiomatic set theory system MS. |
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