Non-reflection of the bad set for check Itheta[lambda] and pcf
Abstract
We reconsider here the following related pcf questions and make some advances: (Q1) concerning the ideal check Ikappa [lambda] how much reflection do we have for the bad set Sbdlambda, kappa subseteq delta < lambda : cf(delta)= kappa assuming it is well defined? (Q2) for an ideal J on kappa how large are SbdJ[f],SchJ[f] for f=< falpha : alpha<lambda > which is <J-increasing and cofinal in (prod limitsi< kappa lambdai,<J) ? (Q3) are there somewhat free black boxes?
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