The following is stated as Theorem VI.5.8 in the newer edition of the book "Almost Free Modules" by Eklof and Mekler, but no proof is given and no precise reference is given. Presumably it comes from Shelah's book, "Cardinal Arithmetic," but that book has 500 pages. I would like to know precisely where in that book I can find the result.
Let $\mu$ be a singular cardinal of cofinality $\kappa$ and let $I$ be the ideal of subsets of $\kappa$ of cardinality less than $\kappa$. Let $<\lambda_i: i<\kappa>$ be a strictly increasing sequence of regular cardinals whose supremum if $\mu$. Let $\tau=\mu^+$.
A "scale" for $\mu$ is a sequence $\bar f=<f_\alpha:\alpha<\tau>$ such that each $f_\alpha\in\prod_{i<\kappa}\lambda_i$ and some other properties hold.
We say $\delta\in\tau$ is a "good point" of $\bar f$ if $\delta$ is a limit and there is a cofinal subset $\Xi$ of $\delta$ and there is $\sigma<\kappa$ such that for all $\alpha<\beta$ in $\Xi$, $f_\alpha(i)<f_\beta(i)$ for all $i>\sigma$.
Shelah's result is that if $\delta<\tau$ is a limit of cofinality greater than $\lambda$ which is not good, then there is a club $C$ in $\delta$ such that no $\alpha\in C$ is good. [I do not know what $\lambda$ is.]