AD+

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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:

  1. Every set of reals is ∞-Borel.
  2. For any ordinal λ less than Θ, any subset A of 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.

See also[edit]

References[edit]

  • W.H. Woodin The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal (1999 Walter de Gruyter) p. 618