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In a handwtitten note of 1975, Leo Harrington sketched a construction of amodel of ZFC (no large cardinals or anything beyond ZFC!) in which$\mathbf\Pi^1_3$-Separation holds but $\mathbf\Sigma^1_3$-Reduction fails. Theresult has never appeared in a journal or book publication except for a few ofold references.

On Harrington's model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami