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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Heike Mildenberger and Saharon Shelah
Journal: Trans. Amer. Math. Soc. 361 (2009), 2305-2317
MSC (2000): Primary 03E35, 03E17, 03E75, 54D40
Published electronically: December 11, 2008
MathSciNet review: 2471919
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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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Additional Information

Heike Mildenberger
Affiliation: Kurt Gödel Research Center for Mathematical Logic, Universität Wien, Währinger Str.\ 25, 1090 Wien, Austria
Email: heike@logic.univie.ac.at

Saharon Shelah
Affiliation: Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel – and – Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
Email: shelah@math.huji.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04806-X
PII: S 0002-9947(08)04806-X
Received by editor(s): November 16, 2006
Published electronically: December 11, 2008
Additional Notes: The first author was partially supported by the Landau Center.
The second author’s research was partially supported by the United States-Israel Binational Science Foundation (Grant no. 2002323). This is the second author’s publication no. 894.
Dedicated: Dedicated to Andreas Blass on the occasion of his 60th birthday.
Article copyright: © Copyright 2008 American Mathematical Society