# Sh:498

- Jin, R., & Shelah, S. (1994).
*Essential Kurepa trees versus essential Jech-Kunen trees*. Ann. Pure Appl. Logic,**69**(1), 107–131. arXiv: math/9401217 DOI: 10.1016/0168-0072(94)90021-3 MR: 1301608 -
Abstract:

By an \omega_1–tree we mean a tree of size \omega_1 and height \omega_1. An \omega_1–tree is called a Kurepa tree if all its levels are countable and it has more than \omega_1 branches. An \omega_1–tree is called a Jech–Kunen tree if it has \kappa branches for some \kappa strictly between \omega_1 and 2^{\omega_1}. A Kurepa tree is called an essential Kurepa tree if it contains no Jech–Kunen subtrees. A Jech–Kunen tree is called an essential Jech–Kunen tree if it contains no Kurepa subtrees. In this paper we prove that (1) it is consistent with CH and 2^{\omega_1}>\omega_2 that there exist essential Kurepa trees and there are no essential Jech–Kunen trees, (2) it is consistent with CH and 2^{\omega_1}>\omega_2 plus the existence of a Kurepa tree with 2^{\omega_1} branches that there exist essential Jech–Kunen trees and there are no essential Kurepa trees. In the second result we require the existence of a Kurepa tree with 2^{\omega_1} branches in order to avoid triviality. - published version (25p)

Bib entry

@article{Sh:498, author = {Jin, Renling and Shelah, Saharon}, title = {{Essential Kurepa trees versus essential Jech-Kunen trees}}, journal = {Ann. Pure Appl. Logic}, fjournal = {Annals of Pure and Applied Logic}, volume = {69}, number = {1}, year = {1994}, pages = {107--131}, issn = {0168-0072}, doi = {10.1016/0168-0072(94)90021-3}, mrclass = {03E35 (03E05 03E50)}, mrnumber = {1301608}, mrreviewer = {Andrzej Szyma\'nski}, doi = {10.1016/0168-0072(94)90021-3}, note = {\href{https://arxiv.org/abs/math/9401217}{arXiv: math/9401217}}, arxiv_number = {math/9401217} }