uniform ultrafilter; linked family
We shall show that there is an ultrafilter on singular $\kappa$ with countable cofinality, which cannot be reached from the set of all subuniform ultrafilters by iterating the closure of sets of size $<\kappa$.
[CN] Comfort W.W., Negrepontis S.: The Theory of Ultrafilters
. Springer, New York, Heidelberg, Berlin (1974). MR 0396267
| Zbl 0298.02004