Axiom of real determinacy explained

In mathematics, the axiom of real determinacy (abbreviated as AD_R) is an axiom in set theory.^[1] 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.

See also

• AD⁺
• Axiom of projective determinacy
• Topological game

Notes and References

1. Ikegami . Daisuke . de Kloet . David . Löwe . Benedikt . 2012-11-01 . The axiom of real Blackwell determinacy . Archive for Mathematical Logic . en . 51 . 7 . 671–685 . 10.1007/s00153-012-0291-x . 1432-0665. free .