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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stable Kneser hypergraphs and ideals in $ \mathbb{N}$ with the Nikodým property


Authors: Noga Alon, Lech Drewnowski and Tomasz Łuczak
Journal: Proc. Amer. Math. Soc. 137 (2009), 467-471
MSC (2000): Primary 05A17, 05C15, 11B05
Published electronically: August 19, 2008
MathSciNet review: 2448565
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Abstract: We use stable Kneser hypergraphs to construct ideals in $ \mathbb{N}$ which are not nonatomic yet have the Nikodým property.


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Additional Information

Noga Alon
Affiliation: Schools of Mathematics and Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel – and – Institute for Advanced Study, Princeton, New Jersey 08540
Email: nogaa@tau.ac.il

Lech Drewnowski
Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Email: drewlech@amu.edu.pl

Tomasz Łuczak
Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Email: tomasz@amu.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09588-9
PII: S 0002-9939(08)09588-9
Keywords: Kneser graph, divergent series, chromatic number, Nikod\'ym property
Received by editor(s): January 22, 2008
Published electronically: August 19, 2008
Additional Notes: The first author is supported by the Israel Science Foundation, by a USA-Israeli BSF grant, by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University, and by the Von Neumann Fund
The third author is supported by the Foundation for Polish Science
Communicated by: Jim Haglund
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.