AD+
# AD+

In set theory, $AD^+$ is an extension, proposed by W. Hugh Woodin, to the axiom of determinacy. The axiom, which is to be understood in the context of ZF plus $DC_{\mathbb{R}$$}$ (the axiom of dependent choice for real numbers), states two things:

* Every set of reals is ∞-Borel.
* For any ordinal λ less than Θ, any subset A of $ω^ω,$ and any continuous function $π:λ^ω→ω^ω,$ the preimage $π^{−1}[A]$ is determined. (Here $λ^ω$ is to be given the product topology, starting with the discrete topology on λ.)

The second clause by itself is referred to as ordinal determinacy.

