On Jónsson cardinals with uncountable cofinality
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 \(\kappa\).
scientific article; zbMATH DE number 3930996