Some results on consecutive large cardinals. II: Applications of Radin forcing
type: Item
instance of: scholarly article
title: Some results on consecutive large cardinals. II: Applications of Radin forcing
zbMATH Open document ID: 0603.03016
DOI: 10.1007/BF02774081
author: Arthur W. Apter
published in: Israel Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: [For Part I see Ann. Pure Appl. Logic 25, 1-17 (1983; Zbl 0548.03030).] Let \(\kappa\) be a 3 huge cardinal in a countable model V of ZFC, and let A and B be subsets of the successor ordinals \(<\kappa\) so that \(A\cup B=\{\alpha <\kappa:\alpha\) is a successor ordinal\(\}\). Using techniques of Gitik, we construct a choiceless model \(N_ A\) of ZF of height \(\kappa\) so that \(N_ A\vDash ''ZF + \neg AC_{\omega} + For\alpha\in A\), \(\aleph_{\alpha}\) is a Ramsey cardinal \(+ For\beta\in B\), \(\aleph_{\beta}\) is a singular Rowbottom cardinal which carries a Rowbottom filter \(+ For\gamma\) a limit ordinal, \(\aleph_{\gamma}\) is a Jonsson cardinal which carries a Jonsson filter''.
Mathematics Subject Classification ID: 03E55
zbMATH DE Number: 3972853
zbMATH Keywords: huge cardinal
zbMATH Keywords: successor ordinals
zbMATH Keywords: choiceless model
zbMATH Keywords: Ramsey cardinal
zbMATH Keywords: singular Rowbottom cardinal
zbMATH Keywords: Rowbottom filter
zbMATH Keywords: limit ordinal
zbMATH Keywords: Jonsson cardinal
zbMATH Keywords: Jonsson filter
MaRDI profile type: Publication
cites work: Some results on consecutive large cardinals
cites work: Successive large cardinals
cites work: The generalized continuum hypothesis can fail everywhere
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full work available at URL: https://doi.org/10.1007/bf02774081
OpenAlex ID: W2008321373
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description: scientific article; zbMATH DE number 3972853