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