On successors of Jonsson cardinals

We show that, like singular cardinals, and weakly compact cardinals, Jensen 's core model K for measures of order zero [4] calculates correctly the suc cessors of Jonsson cardinals, assuming O-Sword does not exist. Namely, if k is a Jonsson cardinal then k(+) = k(+K), provided that there is no non-tri vial elementary embedding j : K --> K. There are a number of related result s in ZFC concerning p(k) in V and inner models, for k a Jonsson or singular cardinal.