TITLE: Countable paracompactness, normality and locally countable open covers
QUESTION [6 upvotes]: (repost from the topology Q&A board)
I have a (T_1), Normal, countably paracompact space X. I would like to know if every locally countable open cover of X (i.e. an open cover such that every x in X has a neighbourhood which intersects only countably many members of the cover) has a locally finite refinement.
My suspicion is that the answer is a resounding no, but every time I try to construct a counterexample it starts to seem more plausible. 
If the answer does turn out to be yes I'd love to know if it generalises from aleph_0 to arbitrary cardinals.

REPLY [4 votes]: In Caryn Navy's thesis under Mary Ellen Rudin she constructed several spaces that are normal, countably paracompact and paralindelöf (every cover has a locally countable refinement) but not paracompact.
All such spaces provide counterexamples (we can refine a cover without a locally finite refinement to a locally countable one and then we cannot continue...)
I'm not sure (as I do not have access to the PhD-thesis in question, and I only know it from references like http://www1.elsevier.com/homepage/sac/opit/10/article.pdf) whether these examples are all under extra set-theoretic assumptions (like MA + non-CH) or whether there are absolute ones as well.