Axiom of real determinacy

In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory. It states the following:

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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.