Notes on subtlety and ineffability in Pκλ

Archive for Mathematical Logic 44 (5):619-631 (2005)
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Abstract.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. (ii) The ideal is not strongly subtle} is not λ-saturated, and completely ineffable ideal is not precipitous. (iii) In case that λ<κ=2λ, almost λ-ineffability coincides with λ-ineffability. (iv) It is not provable that κ is λ<κ-ineffable whenever κ is λ-ineffable.



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References found in this work

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 - Mathematical Logic Quarterly 31 (25‐28):393-401.
Pxδ-Generalizations of Weak Compactness.Donna M. Carr - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (25-28):393-401.

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