Dualization conjecture for the Raisonnier ideal and the null ideal

Let d4a9d4a9 be the Raisonnier ideal, let d4a1d4a1 be the null ideal, and write cov(d4a9){\rm cov}(d4a9) and cof(d4a1){\rm cof}(d4a1) for their covering and cofinality numbers. Let d53dd53d denote the dominating number.

Dualization conjecture.

cov(d4a9)cof(d4a1).{\rm cov}(d4a9) \leq {\rm cof}(d4a1).

Consequently,

cof(d4a1)=max{cov(d4a9),d53d}.{\rm cof}(d4a1)=\max\{{\rm cov}(d4a9),d53d\}.

This conjecture proposes a dual form of the paper's lemma asserting that the additivity of the null ideal is at most the uniformity of the Raisonnier ideal. Its resolution would clarify the relationship between cardinal characteristics associated with the Raisonnier ideal and Lebesgue null sets.

Sources & referencesView supporting material

Primary source

Spyridon Dialiatsis and Yurii Khomskii, “Combinatorial Properties of the Raisonnier Filter”, arXiv:2602.23340 (2026).

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