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Projective determinacy
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In [[mathematical logic]], '''projective determinacy''' is the special case of the [[axiom of determinacy]] applying only to [[projective set]]s. The '''axiom of projective determinacy''', abbreviated '''PD''', states that for any two-player infinite game of [[perfect information]] of length [[Ξ© (ordinal number)|Ο]] in which the players play [[natural number]]s, if the victory set (for either player, since the projective sets are closed under complementation) is projective, then one player or the other has a [[winning strategy]]. The axiom is not a theorem of [[ZFC]] (assuming ZFC is consistent), but unlike the full axiom of determinacy (AD), which contradicts the [[axiom of choice]], it is not known to be inconsistent with ZFC. PD follows from certain [[large cardinal]] axioms, such as the existence of infinitely many [[Woodin cardinal]]s.
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