Sealed Kurepa Trees

Itamar Giron; Yair Hayut

Sealed Kurepa Trees

Logic 2024-01-02 v1

Authors: Itamar Giron , Yair Hayut

Abstract

In this paper we investigate the problem of the distributivity of Kurepa trees. We show that it is consistent that there are Kurepa trees and for every Kurepa tree there is a small forcing notion which adds a branch to it without collapsing cardinals. On the other hand, we derive a proper forcing notion for making an arbitrary Kurepa tree into a non-distributive tree without collapsing $\aleph_1$ and $\aleph_2$ .

Keywords

phylogenetic trees

Cite

@article{arxiv.2401.00572,
  title  = {Sealed Kurepa Trees},
  author = {Itamar Giron and Yair Hayut},
  journal= {arXiv preprint arXiv:2401.00572},
  year   = {2024}
}