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Non-reflection of the bad set for \(\check{I}_\theta[\lambda]\) and pcf. (English) Zbl 1324.03014
Summary: 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 \(S^{\text{bd}}_{\lambda,\kappa} \subseteqq \{\delta < \lambda : \text{cf} (\delta) = \kappa \}\) assuming it is well defined (for transparency only)?
(Q2)
are there somewhat free black boxes?
The advances in (Q2) will be used in subsequent for constructions of abelian groups and modules.

MSC:
03E04 Ordered sets and their cofinalities; pcf theory
03E05 Other combinatorial set theory
MathOverflow Questions:
PCF theory and good points in scales
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