# Sh:469

• Jin, R., & Shelah, S. (1992). Planting Kurepa trees and killing Jech-Kunen trees in a model by using one inaccessible cardinal. Fund. Math., 141(3), 287–296.
• Abstract:
By an \omega_1–tree we mean a tree of power \omega_1 and height \omega_1. Under CH and 2^{\omega_1}>\omega_2 we call an \omega_1–tree a Jech–Kunen tree if it has \kappa many branches for some \kappa strictly between \omega_1 and 2^{\omega_1}. In this paper we prove that, assuming the existence of one inaccessible cardinal,

(1) it is consistent with CH plus 2^{\omega_1}>\omega_2 that there exist Kurepa trees and there are no Jech–Kunen trees,

(2) it is consistent with CH plus 2^{\omega_1}=\omega_4 that only Kurepa trees with \omega_3 many branches exist.

• Version 1994-01-28_10 (11p) published version (10p)
Bib entry
@article{Sh:469,
author = {Jin, Renling and Shelah, Saharon},
title = {{Planting Kurepa trees and killing Jech-Kunen trees in a model by using one inaccessible cardinal}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {141},
number = {3},
year = {1992},
pages = {287--296},
issn = {0016-2736},
mrnumber = {1199241},
mrclass = {03E35 (03E50 03E55)},
doi = {10.4064/fm-141-3-287-296},
note = {\href{https://arxiv.org/abs/math/9211214}{arXiv: math/9211214}},
arxiv_number = {math/9211214}
}