Shelah's work on non-semi-proper iterations. I
type: Item
instance of: scholarly article
title: Shelah's work on non-semi-proper iterations. I
zbMATH Open document ID: 1153.03037
author: Chaz Schlindwein
published in: Archive for Mathematical Logic
publication date: 2008-09-12T00:00:00Z
review text: The author reworks results of Shelah concerning non-semi-proper iterations. It is shown that any forcing notion satisfying a certain condition preserves \(\omega_1\) (and, assuming CH, adds no reals). Namba forcing satisfies the condition, and for each stationary \(W\subseteq \{ \alpha < \omega_2 : \text{cf} (\alpha) = \omega\}\), so does \(P[W]\) (\(P[W]\) is the set of all countable closed subsets of \(W\), ordered by reverse end-extension). The main result asserts that the condition is preserved for appropriate RCS iterations.
reviewed by: Pierre Matet
Mathematics Subject Classification ID: 03E40
zbMATH DE Number: 5343895
zbMATH Keywords: revised countable support iteration
zbMATH Keywords: Namba forcing
MaRDI profile type: Publication
full work available at URL: s00153-008-0099-x
OpenAlex ID: W1975924110
cites work: Q3852172
cites work: Shelah's work on non-semi-proper iterations, II
cites work: Proper forcing
cites work: Q4375363
DOI: 10.1007/S00153-008-0099-X
description: scientific article; zbMATH DE number 5343895