Abstract.
We address partition problems of Erdös 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.
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Received: 27 June 2001 / Revised version: 5 December 2001 / Published online: 4 February 2003
The first author was partially supported by NSF grant DMS-0101155 and the Equipe d'Analyse Univ. of Paris 6. The second author was partially supported by NSF grants DMS-0072560 and DMS-9704477.
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Foreman, M., Hajnal, A. A partition relation for successors of Large Cardinals. Math Ann 325, 583–623 (2003). https://doi.org/10.1007/s00208-002-0323-7
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DOI: https://doi.org/10.1007/s00208-002-0323-7