Projective Determinacy

Some articles on projective determinacy, projective:

Determinator - Determinacy and Large Cardinals - Projective Determinacy
... are infinitely many Woodin cardinals, then projective determinacy holds that is, every game whose winning condition is a projective set is determined ... From projective determinacy it follows that, for every natural number n, there is a transitive inner model which satisfies that there are n Woodin cardinals ...
Second-order Arithmetic - Projective Determinacy
... Projective determinacy is the assertion that every two-player perfect information game with moves being integers, game length ω and projective payoff ... set otherwise, the second player wins.) A set is projective iff (as a predicate) it is expressible by a formula in the language of second order arithmetic, allowing real numbers as parameters, so projective ... of Z2 and even ZFC but are provable from projective determinacy ...