Notes on the partition property of Pκλ

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.