The Non—stantard Models of Axiom System for Set Theory——The Normal Fuzzy Set Structures
ZHANG JINWEN The Institute of Software Academia Sinica Bei jing, China
This paper consists of 3 sections. In the first one, using the method of transfinite recursion on the ordinals, we have defined fuzzy sets of all ranks and class F of all fuzzy sets. In the second section we havn defined fuzzy membership relation and fuzzy equalness relation. And then we deve-loped the normal fuzzy set structure F, and some elementary properties of it. In thelast section,we have proven the main theorems in the paper: F, is a non-standard model of the axiom system ZFU for set theory with the urelements. Hence, all concepts and theorems in Cantor's set theory hold in the system F,.