English

Entangledness in Suslin lines and trees

Logic 2020-04-28 v2

Abstract

We introduce the idea of a weakly entangled linear order, and show that it is consistent for a Suslin line to be weakly entangled. We generalize the notion of entangled linear orders to ω1\omega_1-trees, and prove that an ω1\omega_1-tree is entangled iff it is free. We force the existence of a Suslin tree which is nn-entangled, but all of whose derived trees of dimension n+1n+1 are special, for any positive n<ωn < \omega.

Keywords

Cite

@article{arxiv.1910.08793,
  title  = {Entangledness in Suslin lines and trees},
  author = {John Krueger},
  journal= {arXiv preprint arXiv:1910.08793},
  year   = {2020}
}
R2 v1 2026-06-23T11:48:35.764Z