A hierarchy of filters smaller than \(CF_{\kappa\lambda}\) (Q678253)

A hierarchy of filters on \({\mathcal P}_\kappa\lambda\) is presented which corresponds to the length of diagonal intersections under which the filters are closed. The minimal seminormal ideal is also studied. Its precise description changes according to \(cf(\lambda)\) although we can write it in a single form as well. It is also shown that a nonnormal seminormal ideal extending the nonstationary ideal exists if and only if \(\lambda\) is regular.