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  "body": "\n## Summary\n\nVon Neumann–Bernays–Gödel set theory, NBG, is an axiomatic [[set theory|RTHHCX84HN]] whose objects are [[classes|Y48FA69563]].\nIn it, sets are the classes that are members of other classes.\nIt proves the same statements about sets as [[Zermelo–Fraenkel set theory|0HE5WDQ9FJ]] with choice.\nUnlike ZFC, it can be given by finitely many axioms.\nIt lets one speak directly about large collections, such as the class of all sets or of all groups.\n\n## Explanations\n\n### L1 human\n\nIn ZFC, a phrase such as \"the collection of all sets\" is only a way of talking.\nNBG makes such collections into real objects, called classes.\nA class that is small enough to belong to another class is a set, and the others are proper classes.\nProper classes cannot be elements, so Russell's paradox does not arise.\nCategory theory often uses this setting to talk about the category of all sets.\n",
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