On the axiom of union
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In this paper, we study the union axiom of ZFC. After a brief introduction, we sketch a proof of the folklore result that union is independent of the other axioms of ZFC. In the third section, we prove some results in the theory T:= ZFC minus union. Finally, we show that the consistency of T plus the existence of an inaccessible cardinal proves the consistency of ZFC.
KeywordsAxiom of union Transitive closure Inaccessible cardinal
Mathematics Subject Classification (2000)Primary: 03E30 Secondary: 03E35
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