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基于模型论的非良基性的集合论模型分析

Analysis of set theory model based on model theory

Theoretical Mathematics Study / 2019,1(2): 40-50 / 2019-12-27 1213 1186

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• Authors: 余亮
• Information:

  贵州工程应用技术学院，毕节

• Keywords:
  unwell-founded; set theory model; outer set; inner set
  非良基性; 集合论模型; 外集合; 内集合
• Abstract: New set theory paradox is given in this paper. The existence of a set theory model is proved, where exists an infinite descending outer sequence with respect to ∈ relation of the model. This paper also proves that this kind of sequences may be inserted into well-ordered sets and classes like ω, ω1 , the class of all ordinal numbers ON and the class of all cardinal numbers N of the new model. It is also possible to insert such a sequence into the end section of an uncountable ascending sequence with respect to ∈ relation of the model like ω1. This paper for the first time defines and gives an example for an outer set that is not an inner set in a set theory model. 给出一个新的集合论悖论。用模型论方法证明了非良基性的集合论模 型的存在性。这个模型中存在对∈关系下降的无限元素外序列。还证明可以存 在集合论模型，其中 ω，ω 1 等集合，ON 和 N 等类的内部都存在对∈关系无 限递降的元素外序列。这种对∈关系是无限递降的外序列还可以插入于一个没 有可数共尾的对∈是上升的序列的后面，插入后成为同名集合的一部分。用这 种模型第一次定义并给出了外集合不是内集合的例子。
• DOI: https://doi.org/10.35534/tms.0102007c
• Cite: 余亮．基于模型论的非良基性的集合论模型分析［J］．理论数学前沿，2019，1（2）：40-50．