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。