Abstract
AbstractLet $\kappa $ be a regular uncountable cardinal, and a cardinal greater than or equal to $\kappa $ . Revisiting a celebrated result of Shelah, we show that if is close to $\kappa $ and (= the least size of a cofinal subset of ) is greater than , then can be represented (in the sense of pcf theory) as a pseudopower. This can be used to obtain optimal results concerning the splitting problem. For example we show that if and , then no $\kappa $ -complete ideal on is weakly -saturated.
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