We investigate the partition property of Pκλ. Main results of this paper are as follows: (1) If λ is the least cardinal greater than κ such that Pκλ carries a (λ <κ, 2)-distributive normal ideal without the partition property, then λ is Π n 1-indescribable for all n < ω but not Π 1 2 -indescribable. (2) If cf(λ) ≥ κ, then every ineffable subset of Pκλ has the partition property. (3) If cf(λ) ≥ κ, then the completely ineffable ideal over Pκλ has the partition property.
- Partition property
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