nals. We thank Peter Nyikos for referring us to [@G], where that failure is used to construct a locally compact, locally countable, normal, non-paracompact space $X$ on $\kappa^+\times\omega_1$, where $\kappa^+$ is the successor of a singular strong limit cardinal of countable cofinality, such that the spaces $X_\alpha=\alpha\times\omega$ are metrizable for all $\alpha\in\kappa^+$. It follows that closed subspaces of $X$ of size $\leq 2^{\aleph_0}$ are locally compact and metrizable, so satisfy the MOP by \[lem6\]. On the other hand,

If a Hausdorff space $Z$ is locally countable, locally compact, and closed subspaces of $\leq 2^{\aleph_0}$ have the MOP, then $Z$ has the MOP.

It follows that $X$ has the MOP.\
With MM$(S)[S]$ we have:

$(S)[S]$ implies that if $X$ is normal, locally compact, locally countable, and closed subspaces of size $\leq 2^{\aleph_0}$ are metrizable, then $X$ is metrizable.

By the preceding proof, $X$ has the MOP. By \[thm35\], to get that $X$ is paracompact, it suffices to show that countable subspaces of $X$ have Lindelöf closures. But if $Y$ is a countable subset of $X$, $|\overline{Y}|\leq 2^{\aleph_0}$ and hence is separable metrizable and hence Lindelöf. Once we have $X$ paracompact, it follows that $X$ is a topological sum of $\sigma$-compact subspaces. But each of these has size $\leq 2^{\aleph_0}$ and so is metrizable.

**Axiom R** precludes stationary non-reflecting sets of $\omega$-cofinal ordinals in $\omega_s$, and hence the locally compact, $\aleph_1$-collectionwise Hausdorff ladder system space built on such a set; we can therefore ask:

Examples
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A question left open in [@LT1] is whether, as was shown for adjoining $\aleph_2$ Cohen subsets of $\omega_1$ in [@T1], forcing with a Souslin tree would make normal spaces of character $\aleph_1$ $\aleph_1$-collectionwise Hausdorff. We shall show that the answer is negative by showing:

$_{\omega_1}(S)[S]$ implies that there is a normal non-$\aleph_1$-collectionwise Hausdorff space of character $\aleph_1$.

Let $S\subse