Foreman, Matthew; Hajnal, Andras A partition relation for successors of large cardinals. (English) Zbl 1024.03050 Math. Ann. 325, No. 3, 583-623 (2003). Summary: We address partition problems of Erdős and Hajnal by showing that \(\kappa^+ \to (\kappa^2+1,\alpha)\) for all \(\alpha < \kappa^+\), if \(\kappa^{<\kappa}=\kappa\) and \(\kappa\) carries a \(\kappa\)-dense ideal. If \(\kappa\) is measurable we show that \(\kappa^+ \to (\alpha)^2_n\) for \(n<\omega\), \(\alpha<\Omega\) where \(\Omega\) is a very large ordinal less than \(\kappa^+\) that is closed under all primitive recursive ordinal operations. Cited in 3 Documents MSC: 03E55 Large cardinals 03E02 Partition relations Keywords:partition relation; measurable cardinal; \(\kappa\)-dense ideal PDFBibTeX XMLCite \textit{M. Foreman} and \textit{A. Hajnal}, Math. Ann. 325, No. 3, 583--623 (2003; Zbl 1024.03050) Full Text: DOI