Notes on the partition property of {\ mathcal {P} _\ kappa\ lambda}

Archive for Mathematical Logic 51 (5-6):575-589 (2012)

We investigate the partition property of ${\mathcal{P}_{\kappa}\lambda}$ . Main results of this paper are as follows: (1) If λ is the least cardinal greater than κ such that ${\mathcal{P}_{\kappa}\lambda}$ carries a (λ κ , 2)-distributive normal ideal without the partition property, then λ is ${\Pi^1_n}$ -indescribable for all n < ω but not ${\Pi^2_1}$ -indescribable. (2) If cf(λ) ≥ κ, then every ineffable subset of ${\mathcal{P}_{\kappa}\lambda}$ has the partition property. (3) If cf(λ) ≥ κ, then the completely ineffable ideal over ${\mathcal{P}_{\kappa}\lambda}$ has the partition property
Keywords $${\mathcal{P}_{\kappa}\lambda}$$  Ineffability  Partition property
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DOI 10.1007/s00153-012-0283-x
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References found in this work BETA

Notes on Subtlety and Ineffability in P Κ Λ.Yoshihiro Abe - 2005 - Archive for Mathematical Logic 44 (5):619-631.
Some Combinatorial Problems Concerning Uncountable Cardinals.Thomas J. Jech - 1973 - Annals of Pure and Applied Logic 5 (3):165.

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Subtlety and Partition Relations.Toshimichi Usuba - 2016 - Mathematical Logic Quarterly 62 (1-2):59-71.

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