### Planting Kurepa trees and killing Jech-Kunen trees in a model by using one inaccessible cardinal

by Jin and Shelah. [JiSh:469]

Fundamenta Math, 1992

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.

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