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The Dialectical Study on Axioms of ZF
Zhao Feng * #
ShanXi Coking Coal FengXi Mining Industry Group
*Correspondence author
#Submitted by
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Funding: none
Opened online:22 December 2010
Accepted by: none
Citation: Zhao Feng.The Dialectical Study on Axioms of ZF[OL]. [22 December 2010] http://en.paper.edu.cn/en_releasepaper/content/4398018
 
 
the bounded variable is presented and the axioms of ZF are studied one by one. In which, the formula of empty set is written as (x∈e) = {e} for any x according to the analyze-ability of set and dialectical relations on propositions. Meanwhile, it is analyzed that four propositions are related to the empty set. Furthermore, the expressions and the arithmeticization formulae of axioms of ZF are showed at the paper. As regards the axiom of infinity the limit of set to vary and the bounded infinity is introduced into discussion and analytical representations of ordinals are given from the analyze-ability of set. Obviously, the analytical theory of sets is stronger than ZF, and it is consistent and compatible with ZF.
Keywords:axioms of ZF; empty set; relation on sets; bounded variable; limt of set; ordinals; well-founded set; singular set
 
 
 

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