What does ZFC stand for in set theory?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

Infinity — infinity Mathematical symbol representing the concept of infinity.

In set theory, ZFC stands for Zermelo-Fraenkel set theory with the axiom of choice.12

The system is named after the mathematicians Ernst Zermelo and Abraham Adolf Fraenkel, who developed the foundational axioms used to define sets and avoid paradoxes associated with "too big" collections, such as the set of all sets. The "C" in the acronym specifically denotes the inclusion of the axiom of choice, which asserts the possibility of selecting an element from every nonempty member of any set. While ZFC is the standard system used for the development of classical set theory, it remains a subject of study regarding its ability to resolve problems like the continuum hypothesis.132