High Quality Content by WIKIPEDIA articles! In the foundations of mathematics, Von Neumann–Bernays–Godel set theory (NBG) is an axiomatic set theory that is a conservative extension of the canonical axiomatic set theory ZFC. A statement in the language of ZFC is provable in NBG if and only if it is provable in ZFC. The ontology of NBG includes proper classes, objects having members but that cannot be members. NBG's principle of class comprehension is predicative; quantified variables in the defining formula can range only over sets. Allowing impredicative comprehension turns NBG into Morse-Kelley set theory (MK). NBG, unlike ZFC and MK, can be finitely axiomatized.

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