Axiom of determinacy

Summary

The axiom of determinacy, written AD, says that every infinite game of natural numbers with perfect information is determined. Jan Mycielski and Hugo Steinhaus proposed it in 1962 as an alternative to the axiom of choice, which it contradicts. In ZF together with AD, every set of real numbers is Lebesgue measurable, has the Baire property and has the perfect set property. AD is studied in models such as $L(\R)$, where it can hold under large cardinal hypotheses.