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Is ZFC with existence of Grothendieck universe (variant: Grothendieck universe containing every given set) provable in ZFC to be equiconsistent with ZFC?

If not, what else it may be equiconsistent with? (And in which formalistic it may be proved?)

  • 5
    ZFC+Inaccsessible or two.2011-08-20
  • 1
    @Asaf Karagila: What is "two" in your comment?2011-08-20
  • 2
    One inaccessible cardinal, or two inaccessible cardinals.2011-08-20

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