AD+ Totally Explained

Everything about Ad totally explained

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 reals), 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 called ordinal determinacy.

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