Shelah's consistency conjecture for large sets of singular cardinals

Let $\theta$ be any uncountable cardinal. Shelah's consistency conjecture for pseudopowers. It is consistent that, for some cardinal $\lambda$, both of the following hold: (A) $\theta\leq\left|\{\mu<\lambda:\operatorname{cf}(\mu)=\aleph_0,\ \operatorname{pp}(\mu)>\lambda\}\right|$; and (B) for some $\lambda$, the set $\{\mu<\lambda:\operatorname{cf}(\mu)>\aleph_0,\ \operatorname{pp}_{\aleph_1\text{--complete}}(\mu)>\lambda\}$ is infinite. The claim concerns consistency results in pcf theory and is stated without a resolution in the paper.