Archive for Mathematical Logic 44 (5):619-631 (2005)

.A type of subtlety for Pκλ called “strongly subtle” is introduced to show almost ineffability is consistencywise stronger than Shelah property. The following are also shown: is strongly subtle” has rather strong consequences. The ideal is not strongly subtle} is not λ-saturated, and completely ineffable ideal is not precipitous. In case that λ<κ=2λ, almost λ-ineffability coincides with λ-ineffability. It is not provable that κ is λ<κ-ineffable whenever κ is λ-ineffable.
Keywords P κ λ  Subtlety  Shelah property  (almost) ineffability  Partition property
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DOI 10.1007/s00153-004-0272-9
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References found in this work BETA

On Strong Compactness and Supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
Pxδ-Generalizations of Weak Compactness.Donna M. Carr - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (25-28):393-401.
Menas' Conjecture and Generic Ultrapowers.Yo Matsubara - 1987 - Annals of Pure and Applied Logic 36:225-234.

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Citations of this work BETA

Hierarchies of Ineffabilities.Toshimichi Usuba - 2013 - Mathematical Logic Quarterly 59 (3):230-237.
Subtlety and Partition Relations.Toshimichi Usuba - 2016 - Mathematical Logic Quarterly 62 (1-2):59-71.

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