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

   

 

More on partitioning triples of countable ordinals


Author: Albin L. Jones
Journal: Proc. Amer. Math. Soc. 135 (2007), 1197-1204
MSC (2000): Primary 03E05, 04A20; Secondary 05A18, 05D10
Published electronically: September 26, 2006
MathSciNet review: 2262926
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Abstract: Consider an arbitrary partition of the triples of all countable ordinals into two classes. We show that either for each finite ordinal $ m$ the first class of the partition contains all triples from a set of type  $ \omega + m$, or for each finite ordinal $ n$ the second class of the partition contains all triples of an $ n$-element set. That is, we prove that $ \omega_1 \to (\omega + m, n)^3$ for each pair of finite ordinals $ m$ and $ n$.


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Additional Information

Albin L. Jones
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-2142
Address at time of publication: 2153 Oakdale Rd., Pasadena, Maryland 21122-5715
Email: alj@mojumi.net

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08538-8
PII: S 0002-9939(06)08538-8
Keywords: Countable ordinals, Ramsey theory, transfinite numbers, triples
Received by editor(s): March 1, 2005
Received by editor(s) in revised form: October 25, 2005
Published electronically: September 26, 2006
Additional Notes: The author would like to thank the University of Kansas for its support of this research.
Communicated by: Julia Knight
Article copyright: © Copyright 2006 by Albin L. Jones