CHEN Dong-li, HAN Chan, MA Chun-hui
(College of Science, Xi′an University of Architecture and Technology, Xi′an 710055, Shaanxi, China)
Abstract:
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.
KeyWords:
individual set; index set; standard universe; nonstandard universe; nonstandard enlarged model
