In mathematics, the axiom of real determinacy (abbreviated as AD_{R}) is an axiom in set theory. It states the following:
Axiom — Consider infinite twoperson games with perfect information. Then, every game of length ω where both players choose real numbers is determined, i.e., one of the two players has a winning strategy.
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.
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