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A categorical characterization of sets among classes. (English) Zbl 0632.18003

The author considers the classes X for which \(2^ X\) exists (small classes) and proves that X is a set if and only if any X-indexed union of small classes is small. One can notice that the existence of small classes which are not sets is considered only in the absence of the axiom of regularity.
Reviewer: I.Tofan

MSC:

18B05 Categories of sets, characterizations
03E65 Other set-theoretic hypotheses and axioms