On Jónsson cardinals with uncountable cofinality
type: Item
instance of: scholarly article
title: On Jónsson cardinals with uncountable cofinality
zbMATH Open document ID: 0582.03035
DOI: 10.1007/BF02760956
author: Jan Tryba
published in: Israel Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The paper contains several results about Jónsson cardinals and Jónsson filters. The author proves that the successor of a regular cardinal cannot be Jónsson. In fact, \(\omega_{\eta +\gamma +1}\) is not Jónsson for \(0\neq \gamma <| \eta |\). With reference to inaccessible Jónsson cardinals it is shown that their Mahlo degrees must be limit. In particular, the first Mahlo cardinal cannot be Jónsson. It is also proved that every singular Jónsson cardinal with uncountable cofinality is the limit of some continuous sequence of smaller Jónsson cardinals. Using weakly normal filters the author shows that if an inaccessible cardinal \(\kappa\) carries a Jónsson filter, then the set of regular Jónsson cardinals below \(\kappa\) is stationary in \(\kappa\).
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 03E05
zbMATH DE Number: 3930996
zbMATH Keywords: Rowbottom cardinal
zbMATH Keywords: regular filter
zbMATH Keywords: Jónsson filters
zbMATH Keywords: successor of a regular cardinal
zbMATH Keywords: Mahlo degrees
zbMATH Keywords: Mahlo cardinal
zbMATH Keywords: weakly normal filters
zbMATH Keywords: inaccessible cardinal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3930996