On the \({\mathbb{I}}\)-condition
type: Item
instance of: scholarly article
title: On the \({\mathbb{I}}\)-condition
zbMATH Open document ID: 0559.03032
DOI: 10.1007/BF02761160
author: S. Shelah
author: Moti Gitik
published in: Israel Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The \({\mathbb{I}}\)-condition on forcing notions which implies that the forcing it satisfies does not add reals, was introduced by \textit{S. Shelah} [Proper forcing (1982; Zbl 0495.03035), Chapter XI {\S}2]. Some examples of forcing notions that can iterate while preserving the \({\mathbb{I}}\)- condition are presented and a new sufficient condition on forcing is formulated for the revised countable support iterations preserving the \({\mathbb{I}}\)-condition.
reviewed by: Petr Stepanek
Mathematics Subject Classification ID: 03E40
zbMATH DE Number: 3891349
zbMATH Keywords: iterated forcing without adding reals
MaRDI profile type: Publication
cites work: A new class of order types
cites work: The nonstationary ideal on \(\aleph _ 2\)
cites work: Two weak consequences of 0#
cites work: Iterated forcing and changing cofinalities
cites work: Proper forcing
description: scientific article; zbMATH DE number 3891349