Abstract
This is an unpolished exposition of some work in the theory of projective ordinals under the hypothesis of definable determinacy. This is understood here as the hypothesis that every set of reals in L[R] is determined. Since the projective ordinals are absolute between the real world and L[R] we carry this study entirely within L[R]. Thus we will use the full Axiom of Determinacy (AD) together with ZF + DC (DC is of course the only choice principle that is preserved under this transition to L[R]).
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