Changing cofinalities and the nonstationary ideal
type: Item
instance of: scholarly article
title: Changing cofinalities and the nonstationary ideal
zbMATH Open document ID: 0649.03040
DOI: 10.1007/BF02782938
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The paper consists of two parts. The first part is of technical character: the author introduces an iterated forcing of Prikry type. In the second part he applies the method introduced in the first part to the study of the ideal of nonstationary sets on a cardinal. The main result is the following theorem: If there is a ``very large'' cardinal \(\kappa\), then there is a forcing notion \({\mathbb{P}}\) such that in \(V^{{\mathbb{P}}}\) there is a stationary set S on \(\kappa\) with the property that forcing with \(NS_{\kappa}| S\) (nonstationary sets on \(\kappa\) restricted to S) preserves the cardinals, does not add bounded subsets of \(\kappa\) and for every regular \(\alpha <\kappa\) there is a forcing condition which forces ``cf \(\kappa\) \(=\alpha ''\).
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 03E40
zbMATH DE Number: 4059389
zbMATH Keywords: Prikry-type iterated forcing
zbMATH Keywords: very large cardinals
zbMATH Keywords: ideal of nonstationary sets on a cardinal
author: Moti Gitik
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02782938
OpenAlex ID: W2090075222
description: scientific article; zbMATH DE number 4059389