  We consider ideals $d^0(\mathcal{V})$ which are generalizations of the ideal
$(v^0)$. We formulate couterparts of Hadamard's theorem. Then, adopting the
base tree theorem and applying Kulpa-Szyma\'nski Theorem, we obtain $
cov(d^0(\mathcal{V}))\leq add(d^0(\mathcal{V}))^+$.
