A new model for all C-sequences are trivial

Joint work with Zhixing You and Jiachen Yuan.

Abstract. We construct a model in which all C-sequences are trivial, yet there exists a $\kappa$-Souslin tree with full vanishing levels. This answers a question from a previous paper, 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, and by analyzing a gallery of $\kappa$-cc forcing extensions of the outcome model.

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