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

Heike Mildenberger; Saharon Shelah

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

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

Heike Mildenberger^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We show that there is a forcing extension in which any two ultrafilters on ω 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.

Original language	English
Pages (from-to)	2305-2317
Number of pages	13
Journal	Transactions of the American Mathematical Society
Volume	361
Issue number	5
DOIs	https://doi.org/10.1090/S0002-9947-08-04806-X
State	Published - May 2009

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

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