Set theory
Set theory
The study of sets as a foundation for mathematics, including infinite cardinal and ordinal numbers and the question of which statements a given axiom system can settle.
What is usually left out
Modern set theory is far more than "collections of objects". Most of its work concerns the structure of infinities and independence results: which statements ZFC decides, and what happens when further axioms are assumed. The naive version collapsed — allowing any describable collection to be a set produces Russell’s paradox, from the set of all sets that do not contain themselves. ZFC’s axioms exist to permit the constructions mathematics needs while blocking that one.