Projective determinacy collapses the inner-model omega-one

If $M$ is projectively well-ordered and projective determinacy holds, then ${\omega }_1^M$ is countable in the ambient universe. Otherwise, selecting with the projective well-order the least $M$-code for each countable ordinal produces an uncountable projective set of unique well-order codes. It has no perfect subset by the boundedness theorem for well-order codes, contradicting the perfect set property implied by projective determinacy.