Ideals which generalize $(v^0)$

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}))^+$.

💡 Research Summary

The paper introduces a family of ideals d⁰(𝓥) that generalize the classical ideal (v⁰). The classical (v⁰) ideal consists of all subsets of the Baire space that are “Ramsey‑null” with respect to the Ellentuck topology; equivalently, it can be described as the collection of sets that are nowhere dense in the sense of infinite partitions of ω. The authors replace the universal family of all infinite subsets of ω by an arbitrary family 𝓥 ⊆