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

 

Partitioning triples and partially ordered sets


Author: Albin L. Jones
Journal: Proc. Amer. Math. Soc. 136 (2008), 1823-1830
MSC (2000): Primary 03E05, 05D10; Secondary 05A18
Published electronically: November 6, 2007
MathSciNet review: 2373614
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Abstract: We prove that if $ P$ is a partial order and $ P \to (\omega)^1_\omega$, then

(a)
$ P \to (\omega + \omega + 1, 4)^3$, and
(b)
$ P \to (\omega + m, n)^3$ for each $ m, n < \omega$.
Together these results represent the best progress known to us on the following question of P. Erdos and others. If $ P \to (\omega)^1_\omega$, then does $ P \to (\alpha, n)^3$ for each $ \alpha < \omega_1$ and each $ n < \omega$?


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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
Email: alj@mojumi.net

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09170-8
PII: S 0002-9939(07)09170-8
Keywords: Countable ordinals, non-special tree, partial order, Ramsey theory, triples
Received by editor(s): September 18, 2006
Received by editor(s) in revised form: March 20, 2007
Published electronically: November 6, 2007
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 2007 Albin L. Jones