AD+ Information
https://en.wikipedia.org/wiki/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:
- 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. CS1 maint: discouraged parameter ( link)