Forcing over L separates Σ¹₃-separation from Π¹₃-reduction for the first time and lifts to models M_n with Woodin cardinals.
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A Failure of $\Pi^1_{n+3}$-Reduction in the Presence of $\Sigma^1_{n+3}$-Separation
Forcing over L separates Σ¹₃-separation from Π¹₃-reduction for the first time and lifts to models M_n with Woodin cardinals.