In set theory
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
(the axiom of dependent choice
), 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[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 called ordinal determinacy.