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:

1. Every set of real numbers is ∞-Borel.
2. For any ordinal λ&nbsp;<&nbsp;Θ, any A&nbsp;⊆&nbsp;ω^ω, and any continuous function π:&nbsp;λ^ω&nbsp;→&nbsp;ω^ω, the preimage π^{−1}<nowiki>[A]</nowiki> 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

• Axiom of projective determinacy
• Axiom of real determinacy
• Suslin's problem
• Topological game

References