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Zbl 0632.18003
Rosický, Jiří
A categorical characterization of sets among classes. (English)
[J] Arch. Math., Brno 23, 117-119 (1987). ISSN 0044-8753; ISSN 1212-5059/e

The author considers the classes X for which $2\sp X$ 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.
[I.Tofan]

MSC 2000:: *18B05 Category of sets
03E65 Other hypotheses and axioms (set theory)

Keywords: power object; small classes; set; axiom of regularity

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