2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68606We give an equivalent, but simpler formulation of the axiom SEP introduced by Juhasz and Kunen. Our formulation shows that many of the consequences of the weak Freese-Nation Property of $\mathcal P(ω)$ already follow from SEP. We show that it is consistent that SEP holds while $\mathcal P(ω)$ fails to have the $(\aleph_1,\aleph_0)$-ideal property, which has been introduced by Hart and Dow . This answers a question addressed independently by Fuchino and by Kunen. We also consider some natural variants of SEP and show that certain changes in the definition of SEP do not lead to a different principle. This answers a question addressed by Blass.Logic03E35; 03E05; 03E17; 03E65text