Axiom of real determinacy

In mathematics, the axiom of real determinacy (abbreviated as AD_R) 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_R is inconsistent with the axiom of choice. It also implies the existence of inner models with certain large cardinals.

AD_R is equivalent to AD plus the axiom of uniformization.