Complete normality and metrization theory of manifolds

A manifold is a connected Hausdorff space in which every point has a neighborhood homeomorphic to Euclidean n-space (n is unique). A space is collectionwise Hausdorff (cwH) if every closed discrete subspace D can be expanded to a disjoint collection of open sets each of which meets D in one point. There are exactly two examples of 1-dimensional nonmetrizable hereditarily normal, hereditarily cwH manifolds: the long line and the long ray. The main new result is that if it is consistent that there is a supercompact cardinal, it is consistent that every hereditarily normal, hereditarily cwH manifold of dimension greater than 1 is metrizable.