Von Neumann-Bernays-Gödel Set Theory

Von Neumann–Bernays–Gödel (NBG) Set Theory is a formal framework for understanding sets—the fundamental objects in mathematics. It extends the more common Zermelo-Fraenkel set theory by including both sets and classes (collections of sets) as basic entities. This allows for a more flexible way to handle very large collections, like "the collection of all sets," without leading to logical paradoxes. NBG's axioms define how sets and classes relate, providing a solid foundation for modern mathematics while avoiding inconsistencies inherent in naive set concepts.