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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 (the axiom of dependent choice for real numbers), states two things:

  1. Every set of reals is ∞-Borel.
  2. For any ordinal λ less than Θ, any subset A of ω, and any continuous function π:λ→ω, the preimage π[A] is determined. (Here λ 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.