# Sh:1110

• Shelah, S., & Spinas, O. Different cofinalities of tree ideals. Preprint.
• 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 \mathcal{I}(\mathbf {Q}) associated with a GTF \mathbf {Q}. We show that if for two GTF’s \mathbf{Q_0} and \mathbf{Q_1} the consistency of add(\mathcal{I}(\mathbf{Q_0})) < add(\mathcal{I}(\mathbf{Q_1})) holds, then we can obtain the consistency of cof(\mathcal{I}(\mathbf{Q_1})) < cof(\mathcal{I} (\mathbf{Q_0})). We also show that cof(\mathcal{I}(\mathbf{Q})) can consistently be any cardinal of cofinality larger than the continuum.
@article{Sh:1110,
}