Archive for Mathematical Logic

, Volume 49, Issue 3, pp 283–289 | Cite as

On the axiom of union

  • Greg Oman


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.


Axiom of union Transitive closure Inaccessible cardinal 

Mathematics Subject Classification (2000)

Primary: 03E30 Secondary: 03E35 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsOhio UniversityAthensUSA

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