Different cofinalities of tree ideals

Saharon Shelah,Otmar Spinas

doi:10.1016/j.apal.2023.103290

Different cofinalities of tree ideals

Saharon Shelah, Otmar Spinas

https://doi.org/10.1016/j.apal.2023.103290

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Journal: Annals of Pure and Applied Logic

Publication Date: May 18, 2023

Affiliation: Hebrew University of Jerusalem, Rutgers, The State University of New Jersey, Kiel University

#Miller Forcing #Classical Tree + Show 1 more

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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.

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