Before revision:  Our work is aimed at producing a (\alpha,\Delta)-kernel of D_P(\kappa), namely a set   such that (after a shift) it holds that (1-\alpha)D_P(\kappa)\subset  (  ) \subset (1+\alpha)D_P(\kappa-\Delta).
After revision:  Our work is aimed at producing a (\alpha,\Delta)-kernel of D_P(\kappa), namely a set  such that (after a shift) it holds that (1-\alpha)D_P(\kappa)\subset  ( \mathsf{CH ) \subset (1+\alpha)D_P(\kappa-\Delta).