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On the axiom of union


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.

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Correspondence to Greg Oman.

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Oman, G. On the axiom of union. Arch. Math. Logic 49, 283–289 (2010).

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  • Axiom of union
  • Transitive closure
  • Inaccessible cardinal

Mathematics Subject Classification (2000)

  • Primary: 03E30
  • Secondary: 03E35