Axiom of real determinacy
Axiom of real determinacy
In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory. It states the following:
The axiom of real determinacy is a stronger version of the axiom-of-determinacy (AD), which makes the same statement about games where both players choose integers; ADR is inconsistent with the axiom of choice. It also implies the existence of inner models with certain large cardinals.
ADR is equivalent to AD plus the axiom of uniformization.