On certain indestructibility of strong cardinals and a question of Hajnal
type: Item
instance of: scholarly article
title: On certain indestructibility of strong cardinals and a question of Hajnal
zbMATH Open document ID: 0663.03041
DOI: 10.1007/BF01624081
author: S. Shelah
author: Moti Gitik
published in: Archive for Mathematical Logic
publication date: 1989-01-01T00:00:00Z
review text: In this paper the authors solve a question of Hajnal. Starting with a model with n strong cardinals they construct a model satisfying the following: for some cardinal \(\lambda\), \(\lambda <\lambda^{\omega}<\lambda^{\omega_ 1}<...<\lambda^{\omega_ n}\) and \(2^{\omega_ i}=\omega_{i+1}\) for \(i\in \omega\). In their model, strongness of \(\kappa\) is indestructible under \(\kappa^+\)-weakly closed forcing notions satisfying the Prikry condition. On the other hand it is known that \(\{\lambda^{\delta}|\) \(2^{\delta}<\lambda \}\) is always finite.
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 4083616
zbMATH Keywords: model with strong cardinals
zbMATH Keywords: weakly closed forcing
zbMATH Keywords: Prikry condition
reviewed by: Martin Weese
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4083616