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Negative partition relations for ultrafilters on uncountable cardinals


Authors: Aki Kanamori and Alan D. Taylor
Journal: Proc. Amer. Math. Soc. 92 (1984), 83-89
MSC: Primary 03E05; Secondary 03E35, 03E55, 04A20
DOI: https://doi.org/10.1090/S0002-9939-1984-0749897-7
MathSciNet review: 749897
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Abstract: Assuming GCH, we prove that if $ \kappa $ is a successor cardinal and $ U$ is a uniform ultrafilter on $ \kappa $, then $ U \nrightarrow {(U,3)^2}$. The case $ \kappa = {\omega _1}$ is an old result of Hajnal. Our proof makes use of several known results concerning nonregular, weakly normal and indecomposable ultrafilters, as well as some negative partition relations for uncountable ordinals.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0749897-7
Article copyright: © Copyright 1984 American Mathematical Society

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