Results for '$${\mathcal{P}_{\kappa}\lambda}$$'

Order:
  1.  48
    Notes on the Partition Property of {\ Mathcal {P} _\ Kappa\ Lambda}.Yoshihiro Abe & Toshimichi Usuba - 2012 - Archive for Mathematical Logic 51 (5-6):575-589.
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  2.  73
    On Skinny Stationary Subsets Of.Yo Matsubara & Toschimichi Usuba - 2013 - Journal of Symbolic Logic 78 (2):667-680.
    We introduce the notion of skinniness for subsets of $\mathcal{P}_\kappa \lambda$ and its variants, namely skinnier and skinniest. We show that under some cardinal arithmetical assumptions, precipitousness or $2^\lambda$-saturation of $\mathrm{NS}_{\kappa\lambda}\mid X$, where $\mathrm{NS}_{\kappa\lambda}$ denotes the non-stationary ideal over $\mathcal{P}_\kappa \lambda$, implies the existence of a skinny stationary subset of $X$. We also show that if $\lambda$ is a singular cardinal, then there is no skinnier stationary subset of $\mathcal{P}_\kappa \lambda$. Furthermore, if $\lambda$ is a strong limit singular cardinal, there (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  3.  27
    Hierarchies of Ineffabilities.Toshimichi Usuba - 2013 - Mathematical Logic Quarterly 59 (3):230-237.