2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152913A property of a filter, a kind of large cardinal property, suffices for the proof in Liu Shelah [LiSh:484] and is proved consistent as required there. A natural property which looks better, not only is not obtained here, but is shown to be false. On earlier related theorems see Gitik Shelah [GiSh310].Logictext