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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Oman, G. On the axiom of union. Arch. Math. Logic 49, 283–289 (2010). https://doi.org/10.1007/s00153-009-0163-1
- Axiom of union
- Transitive closure
- Inaccessible cardinal
Mathematics Subject Classification (2000)
- Primary: 03E30
- Secondary: 03E35