Von Neumann–Bernays–Gödel set theory

Von Neumann–Bernays–Gödel (NBG) set theory is a foundational system for mathematics that extends Zermelo-Fraenkel set theory (ZF) by incorporating classes, which are collections of sets that can be too large to be sets themselves. NBG is often considered a more expressive framework than ZF, while still being able to avoid certain paradoxes that can arise in naive set theories.