Abstract
Using a previously unexplored technique we construct a (transparently) hereditarily normal, collectionwise normal, screenable space Z on P×ω in ZFC. With more effort, the space Z is shown to be hereditarily paracompact and is hereditarily a D-space in ZFC. However, Z is easily shown to be a collectionwise normal, screenable Dowker space and is not a D-space in ZF+AD. We also observe that Z is a monotonically normal Dowker space in ZF+AD. It is known that such do not exist in ZFC. If one wants to avoid large cardinals there is a model due to S. Shelah [16], equiconsistent with ZF, where Z is a CWN screenable Dowker space.
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