Inclusion Relationship between Classical Axiomatic Set Theory and Madium Axiomatic Set Theory
  
Key Words: axiomatic set theory   medium axiomatic set theory.  
Fund Project:
Author NameAffiliation
Zhang Dongmo Dept. of Computer Sci.
Nanjing University of Aeronautics and Astronautics
210016 
Xiao Xi′an Group of Math.
Meteorological College of the Air Force
Nanjing 210012 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.1997.03.030
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