# Sh:498

• Jin, R., & Shelah, S. (1994). Essential Kurepa trees versus essential Jech-Kunen trees. Ann. Pure Appl. Logic, 69(1), 107–131.
• 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.
• Version 1994-01-29_10 (28p) 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},
mrnumber = {1301608},
mrclass = {03E35 (03E05 03E50)},
doi = {10.1016/0168-0072(94)90021-3},
note = {\href{https://arxiv.org/abs/math/9401217}{arXiv: math/9401217}},
arxiv_number = {math/9401217}
}