| 论基础公理与反基础公理 |
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| 引用本文： | 李娜,杜文静. 论基础公理与反基础公理[J]. 逻辑学研究, 2013, 0(2): 1-15 |
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| 作者姓名： | 李娜 杜文静 |
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| 作者单位： | [1]南开大学哲学院 [2]华东政法大学人文学院 |
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| 基金项目： | 国家哲学社科基金项目（08BZX049）; 2012年上海高校青年教师培养资助计划（ZZHDZF12004）; 2012年华东政法大学校级项目（12HZK005）; 2013年高校学校青年骨干教师国内访问学者项目 |
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| 摘 要： | "循环并不可恶"。本文在此基础上讨论基础公理和反基础公理。首先指出基础公理原本就是一条有争议的公理;第二,说明基础公理的局限性;第三,详细论述反基础公理家族中的三个成员,并给出它们两两不相容的一个证明;第四,分析反基础公理导致集合论域在V=WF上不断扩张的方法,并指出这种扩张的方法与数系扩张的方法相同;最后结论:良基集合理论(ZFC)与非良基集合理论(ZFC~-+AFA(或者ZFC和ZFC~-+FAFA或者ZFC和ZFC~-+SAFA))之间的关系类似于欧几里得几何学与非欧几何学之间的关系。
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| 关 键 词： | 非良基集合 基础公理 反基础公理 |
On the Foundation Axiom and the Anti-Founded Axioms |
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| Na Li School of Philosophy,Nankai University Wenjing Du. On the Foundation Axiom and the Anti-Founded Axioms[J]. Studies in Logic, 2013, 0(2): 1-15 |
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| Authors: | Na Li School of Philosophy Nankai University Wenjing Du |
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| Affiliation: | Humanities School,East China University of Political Science and Law |
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| Abstract: | ＂Circle is not vicious＂.Based on this,this paper discusses the foundation axiom and the anti-founded axioms.Firstly,we point out that the foundation axiom is a controversial axiom.Secondly,we exhibit the limit of the foundation axiom.Thirdly,this paper dissertates detailedly three members of the family of the anti-foundation axioms and show that they are incompartible pairwise.Fourthly,we analyze how the anti-foundation axioms lead to extensions of the set universe V = WF,and explain that the method of these extensions is analogous to that of extensions about the number systems.Finally,we conclude that the relation between well-founded set theory（ZFC） and non-well-founded set theory（ZFC~- ＋ AFA（or ZFA and ZFC~- ＋ FAFA or ZFC and ZFC~- ＋ SAFA）） is similar to the relation between Euclidean Geometry and non-Euclidean Geometry. |
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