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On a result of Szemerédi

Published online by Cambridge University Press:  12 March 2014

Albin L. Jones
Albin L. Jones*
Affiliation:
2153 Oakdale Rd. Pasadena, MD 21122, USA, E-mail: alj@mojumi.net, URL: http://www.mojumi.net/~alj
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Abstract

We provide a short proof that if κ is a regular cardinal with κ < c, then

for any ordinal α < min{, κ}. In particular,

for any ordinal α < . This generalizes an unpublished result of E. Szemerédi that Martin's axiom implies that

for any cardinal κ with κ < c.

Keywords

cardinal numbersfilter basesordinal numberspolarized partitionspseudo-intersection numberRamsey theory
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 3 , September 2008 , pp. 953 - 956
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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