English

A new model for all $C$-sequences are trivial

Logic 2025-04-10 v1

Abstract

We construct a model in which all CC-sequences are trivial, yet there exists a κ\kappa-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.

Cite

@article{arxiv.2504.06794,
  title  = {A new model for all $C$-sequences are trivial},
  author = {Assaf Rinot and Zhixing You and Jiachen Yuan},
  journal= {arXiv preprint arXiv:2504.06794},
  year   = {2025}
}

Comments

18 pages

R2 v1 2026-06-28T22:52:12.435Z