Negative partition relations for ultrafilters on uncountable cardinals
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- by Aki Kanamori and Alan D. Taylor PDF
- Proc. Amer. Math. Soc. 92 (1984), 83-89 Request permission
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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- 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