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Does Tarski-Grothendieck set theory can prove the consistency of ZFC?

ejewad
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1 Answers1

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Since TG proves the existence of inaccessible cardinals, the answer is "yes."

Noah Schweber
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    This is correct, but it involves an undesirable detour. The usual definition of Grothendieck universes easily implies that they are models of ZFC. There's no need to use the universes to produce inaccessible cardinals $\kappa$ and then use these cardinals to produce models $V_\kappa$ of ZFC. (With the usual constructions, these $V_\kappa$'s will just be the Grothendieck universes that you started with.) – Andreas Blass Oct 09 '15 at 18:37