Non-reflection of the bad set for {check I}_theta[lambda] and pcf
  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? 
Saharon Shelah
math.LO