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Hierarchies of ineffabilities
Author(s) -
Usuba Toshimichi
Publication year - 2013
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201200003
Subject(s) - lambda , partition (number theory) , mathematics , combinatorics , property (philosophy) , limiting , physics , philosophy , epistemology , optics , mechanical engineering , engineering
We study combinatorial large cardinal properties on \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {P}}_{\kappa } \lambda$\end{document} , such as ineffability, almost ineffability, subtlety, and the Shelah property. We show that, even when λ > κ, the almost ineffability of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {P}}_{\kappa } \lambda$\end{document} does not yield the ineffability of κ. We also show that the Shelah property and the partition property of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {P}}_{\kappa } \lambda$\end{document} do not yield the subtlety of κ.