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 set theory|ZF] plus DC_R, states two things:

Every set of real numbers is ∞-Borel.
For any ordinal λ < Θ, any A ⊆ ω^ω, and any continuous function π: λ^ω → ω^ω, the preimage π⁻¹ is determined.

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