A model in which every Kurepa tree is thick (Q1187540)

If \(2^{\omega_ 1}>\omega_ 2\), then a Kurepa tree is called thick if it is an \(\omega_ 1\) tree with countable levels but with \(2^{\omega_ 1}\) branches; if it has \(\kappa\) branches for \(\omega_ 1<\kappa< 2^{\omega_ 1}\), then it is called a Jech-Kunen tree. In an earlier paper [ibid. 32, 448-457 (1991; Zbl 0748.03034)], the author showed that it is consistent with CH plus \(2^{\omega_ 1}>\omega_ 2\) that there is a thick Kurepa tree with no Jech-Kunen subtrees. Here it is shown that, assuming the existence of two strongly inaccessible cardinals, it is consistent with CH plus \(2^{\omega_ 1}>\omega_ 2\) that there exists a thick Kurepa tree but no Jech-Kunen trees at all.