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In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory.[1] It states the following:
Axiom — Consider infinite two-person 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; 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.
^Ikegami, Daisuke; de Kloet, David; Löwe, Benedikt (2012-11-01). "The axiom of real Blackwell determinacy". Archive for Mathematical Logic. 51 (7): 671–685. doi:10.1007/s00153-012-0291-x. ISSN 1432-0665.
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