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Notes on subtlety and ineffability in Pκλ
Archive for Mathematical Logic 44 (5):619-631 (2005)
Abstract
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.My notes
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Citations of this work
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.
Notes on the partition property of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{P}_\kappa\lambda}$$\end{document}. [REVIEW]Yoshihiro Abe & Toshimichi Usuba - 2012 - Archive for Mathematical Logic 51 (5-6):575-589.
References found in this work
On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
Some combinatorial problems concerning uncountable cardinals.Thomas J. Jech - 1973 - Annals of Mathematical Logic 5 (3):165.
Pxδ-Generalizations of Weak Compactness.Donna M. Carr - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (25-28):393-401.
Combinatorial characterization of $\Pi^11$ -indescribability in $P{\kappa}\lambda$.Yoshihiro Abe - 1998 - Archive for Mathematical Logic 37 (4):261-272.
On the existence of strongly normal ideals overP κ λ.Donna M. Carr, Jean -Pierre Levinski & Donald H. Pelletier - 1990 - Archive for Mathematical Logic 30 (1):59-72.
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