On skinny stationary subsets of Pkλ

Yo Matsubara, Toshimichi Usuba

研究成果: Article

1 引用 (Scopus)

抄録

We introduce the notion of skinniness for subsets ofP ë and its variants, namely skinnier and skinniest. We show that under some cardinal arithmetical assumptions, precipitousness or 2ë-saturation of NSë | X, where NSë denotes the non-stationary ideal over Pë, implies the existence of a skinny stationary subset of X. We also show that if ë is a singular cardinal, then there is no skinnier stationary subset of Pë. Furthermore, if ë is a strong limit singular cardinal, there is no skinny stationary subset of Pë. Combining these results, we show that if ë is a strong limit singular cardinal, then NSë | X can satisfy neither precipitousness nor 2ë-saturation for every stationary X Pë. We also indicate that ë(Eë

元の言語English
ページ(範囲)667-680
ページ数14
ジャーナルJournal of Symbolic Logic
78
発行部数2
DOI
出版物ステータスPublished - 2013 6
外部発表Yes

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Singular Limit
Subset
Saturation
Denote
Imply
Ideal

ASJC Scopus subject areas

  • Logic
  • Philosophy

これを引用

On skinny stationary subsets of Pkλ. / Matsubara, Yo; Usuba, Toshimichi.

:: Journal of Symbolic Logic, 巻 78, 番号 2, 06.2013, p. 667-680.

研究成果: Article

Matsubara, Yo ; Usuba, Toshimichi. / On skinny stationary subsets of Pkλ. :: Journal of Symbolic Logic. 2013 ; 巻 78, 番号 2. pp. 667-680.
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