Forcing over L yields a model of Π¹₃-reduction but not Π¹₃-uniformization from ZFC alone.
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Forcing the $\Pi^1_3$-Reduction Property and a Failure of $\Pi^1_3$-Uniformization
Forcing over L yields a model of Π¹₃-reduction but not Π¹₃-uniformization from ZFC alone.