# 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. arXiv: math/9211214 DOI: 10.4064/fm-141-3-287-296 MR: 1199241 -
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.

- 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}, doi = {10.4064/fm-141-3-287-296}, mrclass = {03E35 (03E50 03E55)}, mrnumber = {1199241}, mrreviewer = {James Baumgartner}, doi = {10.4064/fm-141-3-287-296}, note = {\href{https://arxiv.org/abs/math/9211214}{arXiv: math/9211214}}, arxiv_number = {math/9211214} }