  One issue is whether these are really new axioms or whether they follow from ZFC. One of the earliest results in the subject (due to Gale and Stewart in 1953) is that (in ZFC) all Π̰01 (that is, closed) games are determined. This result was extended to the next few levels of the Borel hierarchy. Finally, in 1974, Martin proved the landmark result that Δ̰11-determinacy is provable in ZFC. It turns out that this result is close to optimal—as one climbs the hierarchy of definability, shortly after Δ̰11 one arrives at axioms that fall outside the provenance of ZFC. For example, this is true of Π̰11-determinacy, PD and ADL(ℝ). Thus, we have here a hierarchy of axioms (including PD and ADL(ℝ)) which are genuine candidates for new axioms. 