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_R (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^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.

See also

• Suslin's problem

References

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