On skinny stationary subsets of Pkλ

Yo Matsubara, Toshimichi Usuba

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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

Original languageEnglish
Pages (from-to)667-680
Number of pages14
JournalJournal of Symbolic Logic
Volume78
Issue number2
DOIs
Publication statusPublished - 2013 Jun
Externally publishedYes

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Singular Limit
Subset
Saturation
Denote
Imply
Ideal

ASJC Scopus subject areas

  • Logic
  • Philosophy

Cite this

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

In: Journal of Symbolic Logic, Vol. 78, No. 2, 06.2013, p. 667-680.

Research output: Contribution to journalArticle

Matsubara, Yo ; Usuba, Toshimichi. / On skinny stationary subsets of Pkλ. In: Journal of Symbolic Logic. 2013 ; Vol. 78, No. 2. pp. 667-680.
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