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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 < Θ, any A ⊆ ω, and any continuous function π: λ → ω, the preimage π is determined. (Here, λ 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

• Woodin, W. Hugh (1999). The axiom of determinacy, forcing axioms, and the nonstationary ideal (1st ed.). Berlin: W. de Gruyter. p. 618. ISBN 311015708X.

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