Some set theories, e.g. NewFoundations, are able to express a set that contains all entities, including itself. In ZermeloFraenkel SetTheory, no such set exists.

In set theories with Urelemente (atoms), the UniversalSet is not the same thing as the SetOfAllSets, because the UniversalSet contains atoms while the SetOfAllSets does not. Think of '''Any''' ''vs'' '''Type''' in a type system with FirstClass types.

See also TopType.

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CategoryMath