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arXiv · 2309.01931

Separating cardinal characteristics of the strong measure zero ideal

Jörg Brendle·Miguel A. Cardona·Diego A. Mejía
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Abstract

Let $\mathcal{SN}$ be the $\sigma$-ideal of the strong measure zero sets of reals. We present general properties of forcing notions that allow to control of the additivity of $\mathcal{SN}$ after finite support iterations. This is applied to force that the four cardinal characteristics associated with $\mathcal{SN}$ are pairwise different: \[\mathrm{add}(\mathcal{SN})<\mathrm{cov}(\mathcal{SN})<\mathrm{non}(\mathcal{SN})<\mathrm{cof}(\mathcal{SN}).\] Furthermore, we construct a forcing extension satisfying the above and Cicho\'n's maximum (i.e.\ that the non-dependent values in Cicho\'n's diagram are pairwise different).

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Jörg Brendle, Miguel A. Cardona, Diego A. Mejía. 2023-09-05. Separating cardinal characteristics of the strong measure zero ideal. https://doi.org/10.1142/s0219061325500126

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