Adé

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 R (the axiom of dependent choice for real numbers), states two things: # Every set of real numbers is ∞-Borel. # For any ordinal λ 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.

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