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 DCR (the axiom of dependent choice for real numbers), states two things: # Every set of real numbers is ∞-Borel. # For any ordinal λ < Θ, any A ⊆ ωω, and any continuous function π: λω → ωω, the preimage π−1[A] is determined. (Here, λω 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.