Universal Set

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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