Non-reflection of the bad set for $\check I_\theta[\lambda]$ and pcf

by Shelah. [Sh:1008]
Acta Math Hungarica, 2013
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[bar f],S^{ch}_J[bar f] for bar 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?

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