SH plus CH does not imply stationary antichains.
Let CH denote the continuum hypothesis, SH Suslin's hypothesis, KH Kurepa's hypothesis, and NSA the statement asserting the existence of an Aronszajn tree in which every antichain \({\mathcal A}\) has the property that \(\{rk(x):x\in{\mathcal A}\}\) is a nonstationary subset of \(\omega_1\). In ``Suslin's hypothesis does not imply stationary antichains'' [Ann. Pure Appl. Logic 64, No. 2, 153--167 (1993; Zbl 0805.03037)] the author established the consistency of ``SH+NSA+not CH''. In the present paper he proves the consistency of ``SH+NSA+CH''. The author points out that ``It appears that it would be quite straightforward to combine the ideas of [\textit{C. Schlindwein}, ``Special non-special \(\aleph_1\)-trees'', Lect. Notes Math. 1401, 160--166 (1989; Zbl 0694.03032)] to obtain a model of SH plus CH plus NSA plus not KH.''
scientific article; zbMATH DE number 2009288
scientific article