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ISSN 1088-6850(e) ISSN 0002-9947(p)

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

Author(s): Heike Mildenberger; Saharon Shelah
Journal: Trans. Amer. Math. Soc. 361 (2009), 2305-2317.
MSC (2000): Primary 03E35, 03E17, 03E75, 54D40
Posted: 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: 10.1090/S0002-9947-08-04806-X
PII: S 0002-9947(08)04806-X
Received by editor(s): November 16, 2006
Posted: 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.
Copyright of article: Copyright 2008, American Mathematical Society

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