### 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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