The near coherence of filters principle does not imply the filter dichotomy principle

Mildenberger, Heike; Shelah, Saharon

doi:10.1090/S0002-9947-08-04806-X

The near coherence of filters principle does not imply the filter dichotomy principle
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by Heike Mildenberger and Saharon Shelah PDF

Trans. Amer. Math. Soc. 361 (2009), 2305-2317 Request permission

Abstract:

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 (1989) of whether the principle of near coherence of filters is strictly weaker than the filter dichotomy principle.

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