摘要
本文证明了在 k-饱和的分析的非标准模型中,~*N,~*Q,~*R,~*N-N,~*Q-Q,~*R-R,~*R 的每个非有限的~*-有限子集,每个单子,每个银河,~*R 的所有单子之集,所有银河之集,~*R 的稠密子集,~*R 中的所有空隙之集的基数均不小于 k;~*R 的Q-拓扑,S-拓扑的基数不小于2~k.
It is shown that in a k-saturated nonstandard model of analysis,each of the following sets has cardinality at least k:~*N,~*Q,~*R,~*N-N,~*Q-Q,~*R-R, a non-finite ~*finite subset of ~*R,a monad of ~*R,a galaxy of ~*R,a dense su- bset of ~*R,the set of monads of ~*R,the set of galaxies of ~*R,the set of gaps in ~*R,the set of gaps in a monad of ~*R,and that each of the Q-topology and S-topology for ~*R has eardinality at least 2~k.
出处
《陕西师大学报（自然科学版）》
CSCD
1990年第1期11-13,共3页
Journal of Shaanxi Normal University(Natural Science Edition)
关键词
非标准模型
超实数域
基数
K-饱和
nonstandard model of analysis
k-saturation
hyperreal numer field
internal set
