In mathematics, the axiom of real determinacy (abbreviated as AD<sub>R</sub>) 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; AD<sub>R</sub> is inconsistent with the axiom of choice. It also implies the existence of inner models with certain large cardinals.
AD<sub>R</sub> is equivalent to AD plus the axiom of uniformization.