A new model for all -sequences are trivial
arXiv:2504.06794
Abstract
We construct a model in which all -sequences are trivial, yet there exists a -Souslin tree with full vanishing levels. This answers a question of Lambie-Hanson and Rinot, and provides an optimal combination of compactness and incompactness. It is obtained by incorporating a so-called mutually exclusive ascent path to Kunen's original forcing construction.
18 pages