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Polarized Partition Relations

James E. Baumgartner and Andras Hajnal
The Journal of Symbolic Logic
Vol. 66, No. 2 (Jun., 2001), pp. 811-821
DOI: 10.2307/2695046
Stable URL: http://www.jstor.org/stable/2695046
Page Count: 11
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Polarized Partition Relations
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Abstract

It is shown that for any cardinal $\kappa, \dbinom{(2^{<\kappa})^{++}} {(2^{<\kappa})^+} \rightarrow \dbinom{\kappa}{\kappa}_{< \mathrm{cf} \kappa}$, and if κ is weakly compact $\dbinom{\kappa^+}{\kappa} \rightarrow \dbinom{\kappa}{\kappa}_{< \kappa}$.

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