摘要
研究了个体集和超滤子与超幂非标准模型的构造.证明了当转换原理成立时,要求构造超结构的基本集是个体集;讨论了个体集和超滤子不同时,标准全域与非标准全域之间的关系,同时给出了超幂非标准模型是其真扩张的充分条件;得到了非标准模型是非标准扩大模型的必要条件是card(I)>N0.
Constructions of ultrapower nonstandard models are discussed.It is proved that if the transfer principle holds,then the basic set of constructing superstructure is the individual set. Based on difference of individual set and ultrafilter,a relation between standard universe and nonstandard universe is discussed,and a sufficient condition for a ultrapower nonstandard model to be its proper extension is given. It is also proved that a necessary condition for a nonstandard model to be a nonstandard enlarged model is card（I）〉 0.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2010年第3期20-23,共4页
Journal of Shaanxi Normal University：Natural Science Edition
基金
陕西省自然科学基金资助项目(2007A12)
西安建筑科技大学青年科技基金资助项目(QN0736
QN0833)
关键词
个体集
指标集
标准全域
非标准全域
非标准扩大模型
individual set
index set
standard universe
nonstandard universe
nonstandard enlarged model
