On successors of Jónsson cardinals (Q1584016)

\(K\) is Jensen's core model for measures of order zero. The authors prove that in \(\text{ZFC} + ``O^{Sword}\) does not exist''~ if \(\kappa\) is a Jónsson cardinal, then \(\kappa^{+}=\kappa^{+ K}\); i.e., under the given conditions, the successors of Jónsson cardinals are correctly computed in \(K\). There are other ZFC results such as: for \(\kappa\) a regular Jónsson cardinal, if \(V_{\kappa}=V_{\kappa}^{K}\) then \(V_{\kappa +1}=V_{\kappa +1}^{K}.\)