Regularity of ultrafilters and the core model
This paper contains the following two important results: (1) If there is no model with a measurable cardinal, then every uniform ultrafilter on a singular cardinal is regular. (2) If there is no inner model with a measurable cardinal and \(\kappa >\omega\) is regular with \((\kappa^+)^ K=\kappa^+\), then every uniform ultrafilter on \(\kappa\) is regular. (So in particular, in the core model K, every uniform ultrafilter is regular.) The author introduces certain combinatorial principles, which are strengthenings of \(\square_{\kappa}\). He shows these hold in K. Then from these combinatorial statements he proves the results about uniform ultrafilters.
scientific article; zbMATH DE number 4083612
scientific article