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Grothendieck Universe and Strongly Inaccessible Cardinals

Equivalence#

The following two axioms are equivalent

  1. For each set \(x\) there is a Grothendieck universe such that \(x\in U\).
  2. For each cardinal \(\kappa\), there is a strongly inaccessible cardinal \(|\lambda|\) that is strictly larger than \(\kappa\).