Positive partition relations for $P_\kappa(\lambda)$

by Matet and Shelah. [MtSh:804]

Let kappa a regular uncountable cardinal and lambda a cardinal > kappa, and suppose lambda^{< kappa} is less than the covering number for category cov (M_{kappa, kappa}) . Then (a) I_{kappa, lambda}^+ mathop {--->} limits^kappa (I_{kappa, lambda}^+, omega +1)^2, (b) I_{kappa, lambda}^+ mathop {--->} limits^kappa [I_{kappa, lambda}^+]_{kappa^+}^2 if kappa is a limit cardinal, and (c) I_{kappa, lambda}^+ mathop {--->} limits^kappa (I_{kappa, lambda}^+)^2 if kappa is weakly compact.


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