Separating cardinal characteristics of the strong measure zero ideal
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915452244983808 |
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| author | Brendle, Jörg Cardona, Miguel A. Mejía, Diego A. |
| author_facet | Brendle, Jörg Cardona, Miguel A. Mejía, Diego A. |
| contents | Let $\mathcal{SN}$ be the $σ$-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 Cichoń's maximum (i.e.\ that the non-dependent values in Cichoń's diagram are pairwise different). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01931 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Separating cardinal characteristics of the strong measure zero ideal Brendle, Jörg Cardona, Miguel A. Mejía, Diego A. Logic 03E17, 03E35, 03E40 Let $\mathcal{SN}$ be the $σ$-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 Cichoń's maximum (i.e.\ that the non-dependent values in Cichoń's diagram are pairwise different). |
| title | Separating cardinal characteristics of the strong measure zero ideal |
| topic | Logic 03E17, 03E35, 03E40 |
| url | https://arxiv.org/abs/2309.01931 |