Possible values for \(2^{\aleph_n}\) and \(2^{\aleph_\omega}\)
type: Item
instance of: scholarly article
title: Possible values for \(2^{\aleph_n}\) and \(2^{\aleph_\omega}\)
zbMATH Open document ID: 0896.03041
DOI: 10.1016/S0168-0072(97)00037-7
author: Carmi Merimovich
author: Moti Gitik
published in: Annals of Pure and Applied Logic
publication date: 1998-02-17T00:00:00Z
review text: Let \(m\) be a natural number with \(m>1\) and let \(\alpha: \omega\to \omega\) be a monotonic function with \(\alpha (n)>n\) for each \(n\). Assuming that \(\kappa\) is a \(P(\kappa)\)-hyper measurable cardinal, the authors build a forcing extension with \(2^{\aleph_n} =\aleph_{\alpha (n)}\) and \(2^{\aleph_\omega} =\aleph_{\omega+n}\). It was shown by Gitik and Magidor that for \(m>2\) this assumption is needed, whereas it can be shown that for \(m=2\) this assumption can be reduced.
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 03E50
zbMATH DE Number: 1109893
zbMATH Keywords: generic extension
zbMATH Keywords: large cardinals
zbMATH Keywords: singular cardinal hypothesis
zbMATH Keywords: forcing extension
reviewed by: Martin Weese
MaRDI profile type: Publication
cites work: A Model in Which GCH Holds at Successors but Fails at Limits
cites work: Q4106202
cites work: Powers of regular cardinals
cites work: The generalized continuum hypothesis can fail everywhere
cites work: The negation of the singular cardinal hypothesis from \(o(\kappa)=\kappa ^{++}\)
cites work: The strength of the failure of the singular cardinal hypothesis
cites work: Q4694295
cites work: Q3852172
cites work: Q4315890
cites work: Set theory. An introduction to independence proofs
cites work: On the singular cardinals problem. I
cites work: On the singular cardinals problem. II
cites work: Indiscernible sequences for extenders, and the singular cardinal hypothesis
cites work: Q5613932
cites work: Proper forcing
cites work: Q4326402
cites work: Q3041184
full work available at URL: s0168-0072(97)00037-7
OpenAlex ID: W590402559
description: scientific article; zbMATH DE number 1109893