ZFC (Zermelo-Fraenkel set theory with the Axiom of Choice)

ZFC is a foundational system for mathematics that uses a precise set of rules to understand and build all mathematical objects. It defines what sets are—collections of objects—and includes axioms that specify how sets can be created, combined, and related. The Axiom of Choice, added to ZF (Zermelo-Fraenkel set theory), allows selecting elements from collections of sets even without explicit rules. Together, ZFC provides a consistent framework to develop most of modern mathematics, ensuring that mathematical statements are well-defined and logical within this shared foundation.