체르멜로-프렝켈 집합론
The theorem is also known for its metamathematical properties. In 1971, before the theorem was proved, Harvey Friedman showed that any proof of the theorem in Zermelo–Fraenkel set theory must make repeated use of the axiom of replacement. Later results showed that stronger determinacy theorems cannot be proven in Zermelo–Fraenkel set theory, although they are relatively consistent with it, if certain large cardinals are consistent.