  Let $\mu < \kappa < \lambda$ be three infinite cardinals, the first two being
regular. We show that if there is no inner model with large cardinals, $u
(\kappa, \lambda)$ is regular, where $u (\kappa, \lambda)$ denotes the least
size of a cofinal subset in $(P_\kappa (\lambda), \subseteq)$, and cf$(\lambda)
\not= \mu$, then (a) the $\mu$-club filters on $P_\kappa (\lambda)$ and
$P_\kappa (u (\kappa, \lambda))$ are isomorphic, and (b) the ideal dual to the
$\mu$-club filter on $P_\kappa (\lambda)$ (and hence the restriction of the
nonstationary ideal on $P_\kappa (\lambda)$ to sets of uniform cofinality
$\mu$) is not $I_{\kappa, \lambda}$-$\frak{b}_{u (\kappa, \lambda)}$-saturated.
