Cardinal invariants on universally null sets

Abstract

We investigate the cardinal invariants on universally null sets. In particular, we prove $\mathfrak{b} < \operatorname{cof}(\mathcal{UN})$ and $\operatorname{non}(\mathcal{N}) = \operatorname{non}(\mathcal{UN}) < \operatorname{cof}(\mathcal{UN})$ in $\mathsf{ZFC}$. Also, assuming $\operatorname{add}(\mathcal{N}) = \mathfrak{c}$, we prove $\operatorname{cof}(\mathcal{UN}) = \mathfrak{d}_\mathfrak{c}$ by adapting Yorioka's technique. Moreover, we prove the consistency of $\operatorname{add}(\mathcal{UN}) < \operatorname{cov}(\mathcal{UN}) < \operatorname{non}(\mathcal{UN}) < \operatorname{cof}(\mathcal{UN})$.

Disclosure

“osium; the conference version was made available only on the conference webpage and was not published in formal proceedings. The author thanks Diego Mejı́a and Tristan van der Vlugt for their helpful comments. Also, the author used ChatGPT, developed by OpenAI, during the preparation of this pa- per as a source of preliminary ideas and heuristic suggestions concerning some of the proofs, and for English-language proofreading. All mathematical arguments were independently ver”

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Classification

Proof ideas or individual proof-step assistance

Multiplier

8

Verified

2026-08-23T18:52:58.062396Z

Structural counts