Hereditarily normal manifolds of dimension > 1 may all be metrizable

TL;DR

This paper investigates whether all hereditarily normal manifolds of dimension greater than one are necessarily metrizable, removing previous assumptions and showing this can be consistent without extra conditions.

Contribution

The authors prove that the assumption of a supercompact cardinal and additional conditions are not necessary for all hereditarily normal manifolds of dimension > 1 to be metrizable.

Findings

It is consistent that all hereditarily normal manifolds of dimension > 1 are metrizable.

Previous assumptions like supercompact cardinals are not required.

The result extends the understanding of the structure of hereditarily normal manifolds.

Abstract

P.J. Nyikos has asked whether it is consistent that every hereditarily normal manifold of dimension > 1 is metrizable, and proved it is if one assumes the consistency of a supercompact cardinal, and, in addition, that the manifold is hereditarily collectionwise Hausdorff. We are able to omit these extra assumptions.