We reconsider here the following related pcf questions and make some advances: (Q1) concerning the ideal { check I}_kappa [lambda] how much reflection do we have for the bad set S^{ bd}_{ lambda, kappa} subseteq { delta < lambda : cf(delta)= kappa} assuming it is well defined? (Q2) for an ideal J on kappa how large are S^{ bd}_J[f],S^{ ch}_J[f] for f=< f_alpha : alpha<lambda > which is <_J-increasing and cofinal in (prod limits_{ i< kappa} lambda_i,<_J) ? (Q3) are there somewhat free black boxes?
Categories: math.LO