Partitioning triples and partially ordered sets
Author:
Albin L. Jones
Journal:
Proc. Amer. Math. Soc. 136 (2008), 18231830
MSC (2000):
Primary 03E05, 05D10; Secondary 05A18
Published electronically:
November 6, 2007
MathSciNet review:
2373614
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We prove that if is a partial order and , then  (a)
 , and
 (b)
 for each .
Together these results represent the best progress known to us on the following question of P. Erdos and others. If , then does for each and each ?
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 P. Erdos and R. Rado, A partition calculus in set theory, Bull. Amer. Math. Soc. 62 (1956), 427489. MR 0081864 (18:458a)
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 Thomas Jech, Set theory, second ed., SpringerVerlag, Berlin, 1997. MR 99b:03061
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 , A short proof of a partition relation for triples, Electronic Journal of Combinatorics 7(1) (2000), 19. MR 1755613 (2001a:03097)
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 , A partition relation for triples using a model of Todorcevic, Discrete Math. 95 (1991), nos. 13, 183191, Directions in infinite graph theory and combinatorics (Cambridge, 1989). MR 1141938 (93i:03065)
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Additional Information
Albin L. Jones
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 660452142
Address at time of publication:
2153 Oakdale Rd., Pasadena, Maryland 21122
Email:
alj@mojumi.net
DOI:
http://dx.doi.org/10.1090/S0002993907091708
PII:
S 00029939(07)091708
Keywords:
Countable ordinals,
nonspecial 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
