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 reals is ∞-Borel.
- 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

## References

- Woodin, W. Hugh (1999).
*The axiom of determinacy, forcing axioms, and the nonstationary ideal*(1st ed.). Berlin: W. de Gruyter. p. 618. ISBN 311015708X.