2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155929The $σ$-ideal $(v^0)$ is associated with the Silver forcing, see \cite{bre}. Also, it constitutes the family of all completely doughnut null sets, see \cite{hal}. We introduce segments and $*$-segments topologies, to state some resemblances of $(v^0)$ to the family of Ramsey null sets. To describe $add(v^0)$ we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen's conjecture $cov(v^0) = add(v^0)$ is confirmed under the hypothesis $t= \min \{\cf (\frak c), r\} $. The hypothesis $h=ω_1$ implies that $(v^0)$ has the ideal type $(\frak c, ω_1,\frak c)$.Accepted for publication in CEJMLogicCombinatoricsGeneral Topology03E35, 03E50, 26A03, 28A05, 54A10text