Different cofinalities of tree ideals

Saharon Shelah, Otmar Spinas*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce a general framework of generalized tree forcings, GTF for short, that includes the classical tree forcings like Sacks, Silver, Laver or Miller forcing. Using this concept we study the cofinality of the ideal I(Q) associated with a GTF Q. We show that if for two GTF's Q0 and Q1 the consistency of add(I(Q0))<add(I(Q1)) holds, then we can obtain the consistency of cof(I(Q1))<cof(I(Q0)). We also show that cof(I(Q)) can consistently be any cardinal of cofinality larger than the continuum.

Original languageEnglish
Article number103290
JournalAnnals of Pure and Applied Logic
Volume174
Issue number8
DOIs
StatePublished - 1 Aug 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

  • Additivity
  • Cofinality
  • Tree forcing
  • Tree ideal

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