Planting Kurepa trees and killing Jech-Kunen trees in a model by using one inaccessible cardinal
Logic
2016-09-06 v1
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.
Keywords
Cite
@article{arxiv.math/9211214,
title = {Planting Kurepa trees and killing Jech-Kunen trees in a model by using one inaccessible cardinal},
author = {Renling Jin and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9211214},
year = {2016}
}