Grothendieck universe Guide, Meaning , Facts, Information and Description
In mathematics, if κ is a strongly inaccessible cardinal, the corresponding Grothendieck universe is the set of all sets with rank less than κ. By a theorem of Mirimanoff, the Grothendieck universe is a set, not a proper class. Since it cannot be proven in ZFC that inaccessible cardinals exist, using a Grothendieck universe in the place of the class of all sets suffices for normal mathematical purposes, rendering proper classes unnecessary. The idea is due to Alexander Grothendieck, who used it as a way of avoiding proper classes in algebraic geometry.
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