In this paper, Peano′s natural number system is constructed in the medium axiomatic set theory (MS). Based on this construction, the definition of well set in MS is redefined, and it is proved that redefined well set satisfies all the axioms of axiomatic set theory system ZFC-(a subsystem of ZFC without the regular axiom). It is concluded, therefore, that the classical axiomatic set theory system ZFC- is a subsystem of the medium axiomatic set theory system MS. |