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 DCR, states two things:
- Every set of reals is ∞-Borel.
- For any ordinal λ less than Θ, any subset A of ωω, and any continuous function π:λω→ωω, the preimage π−1 is determined.
The second clause by itself is referred to as ordinal determinacy.
