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More remarks on the intersection ideal \(\mathcal{M}\cap\mathcal{N}\). (English) Zbl 1424.03020

Given two ideal \(I\) and \(J\) on the Cantor set \(2^\omega\) we say that \(X\in(I,J)^*\) if for all \(A\) in \(I\) the sum \(A+X\) is in \(J\); also, \(I^*\) abbreviates \((I,I)^*\). Answering a question from [the author, Commentat. Math. Univ. Carol. 54, No. 3, 437–445 (2013; Zbl 1289.03031)], the author shows that \((\mathcal{M}\cap \mathcal{N})^*\subseteq \mathcal{N}^*\), where \(\mathcal{M}\) and \(\mathcal{N}\) are the ideals of meager and null sets, respectively. In addition, there is a provisional solution to the question whether it is consistent that every member of \((\mathcal{E},\mathcal{M})^*\) is countable, where \(\mathcal{E}\) is the \(\sigma\)-ideal generated by the \(F_\sigma\)-sets of measure zero.
Reviewer: K. P. Hart (Delft)

MSC:

03E05 Other combinatorial set theory
03E17 Cardinal characteristics of the continuum
03E15 Descriptive set theory

Citations:

Zbl 1289.03031
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References:

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