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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 reals), states two things:## External links

- 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.

- Woodin, W. Hugh (2001). " The Continuum Hypothesis (III)". Slide 8. Accessed on 2 October, 2005.

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Last updated on Saturday September 20, 2008 at 00:16:47 PDT (GMT -0700)

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Last updated on Saturday September 20, 2008 at 00:16:47 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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