Problem #24

Is add(N) < add(UN) consistent?

Open!

Let $\mathrm{add}(\mathcal{N})$ and $\mathrm{add}(\mathcal{UN})$ denote the additivity numbers of the Lebesgue null σ-ideal and the universally null σ-ideal respectively. Is $\mathrm{add}(\mathcal{N})<\mathrm{add}(\mathcal{UN})$ consistent with ZFC?

Set Theory
Descriptive Set Theory

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Notes

Goto [Got26] has attained results on other cardinal characteristics of UN. More open questions about UN can be found in the paper, such as the consistency of $\mathrm{cof}(\mathcal{UN})<\mathfrak{c}$ .

Reference for the problem statement

[Got26]Tatsuya Goto, Cardinal invariants on universally null sets [link]

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