NBG Set Theory

NBG (von Neumann–Bernays–Gödel) set theory is a formal framework for understanding sets, which are collections of objects. It extends basic set theory by distinguishing between sets and classes—large collections that may not themselves be sets. NBG allows mathematicians to carefully manage and avoid certain paradoxes, providing a logical foundation for much of modern mathematics. It keeps the core ideas of sets manageable while allowing for powerful concepts, making it both rigorous and flexible for formal reasoning about collections.