The Near Coherence of Filters Principle does not imply the Filter Dichotomy Principle

by Mildenberger and Shelah. [MdSh:894]
Transactions American Math Soc, 2009
We show that there is a forcing extension in which any two ultrafilters on omega are nearly coherent and there is a non-meagre filter that is not nearly ultra. This answers Blass' longstanding question (cite[3]) whether the principle of near coherence of filters is strictly weaker than the filter dichotomy principle.


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