SH plus CH does not imply stationary antichains.
type: Item
instance of: scholarly article
title: SH plus CH does not imply stationary antichains.
zbMATH Open document ID: 1046.03030
DOI: 10.1016/S0168-0072(03)00057-5
author: Chaz Schlindwein
published in: Annals of Pure and Applied Logic
publication date: 2003-11-25T00:00:00Z
review text: 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.''
reviewed by: Pierre Matet
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E50
Mathematics Subject Classification ID: 03E05
zbMATH DE Number: 2009288
zbMATH Keywords: Aronszajn tree
zbMATH Keywords: Suslin hypothesis
zbMATH Keywords: proper forcing
zbMATH Keywords: continuum hypothesis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2009288