A NEW PARADOX ON UNWELL-FOUNDED SET THEORY MODELS
Luo Libo · Journal of Beijing Normal University · 2009
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.