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Authors:
余亮
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Information:
贵州工程应用技术学院,毕节
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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
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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。
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DOI:
https://doi.org/10.35534/tms.0102007c
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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.