von Neumann-Bernays-Gödel set theory (abbreviated "NBG") is a version of set theory which was designed to give the same results as Zermelo-Fraenkel set theory, but in a more logically elegant fashion. It can be viewed as a conservative extension of Zermelo-Fraenkel set theory in the sense that a statement about sets is provable in NBG if and only if it is provable in Zermelo-Fraenkel set theory.
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