AD+ 2818935 163323717 2007-10-09T13:38:24Z SmackBot 433328 Standard headings &/or gen fixes. 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 [[Zermelo-Fraenkel set theory|ZF]] plus DC<sub>R</sub> (the [[axiom of dependent choice]] for [[real number|reals]]), states two things: # Every [[set]] of reals is [[∞-Borel]]. # For any ordinal λ less than [[Theta (set theory)|Θ]], any subset ''A'' of ω<sup>ω</sub>, and any [[continuous function]] π:λ<sup>ω</sup>→ω<sup>ω</sup>, the [[preimage]] π<sup>-1</sup><nowiki>[A]</nowiki> is [[Determinacy|determined]]. (Here λ<sup>ω</sup> is to be given the [[product topology]], starting with the [[discrete topology]] on λ.) The second clause by itself is called '''''ordinal determinacy'''''. ==External links== *Woodin, W. Hugh (2001). "[http://math.berkeley.edu/~woodin/talks/lc2000.3.pdf The Continuum Hypothesis (III)]". Slide 8. Accessed on [[2 October]], [[2005]]. [[Category:Axioms of set theory]] [[Category:Determinacy]] {{mathlogic-stub}}