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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.09649 |
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| _version_ | 1866914132974895104 |
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| author | Valderrama, David |
| author_facet | Valderrama, David |
| contents | We investigate some variants of the splitting, reaping, and independence numbers defined using asymptotic density. Specifically, we give a proof of Con($\mathfrak{i}<\mathfrak{s}_{1/2}$), Con($\mathfrak{r}_{1/2}<\mathfrak{b}$) and Con($\mathfrak{i}_*<2^{\aleph_0}$). This answers two questions raised in arXiv:1808.02442v3. Besides, we prove the consistency of $\mathfrak{s}_{1/2}^{\infty} < $ non$(\mathcal{E})$ and cov$(\mathcal{E}) < \mathfrak{r}_{1/2}^{\infty}$, where $\mathcal{E}$ is the $σ$-ideal generated by closed sets of measure zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09649 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cardinal invariants related to density Valderrama, David Logic 03E17, 03E35 We investigate some variants of the splitting, reaping, and independence numbers defined using asymptotic density. Specifically, we give a proof of Con($\mathfrak{i}<\mathfrak{s}_{1/2}$), Con($\mathfrak{r}_{1/2}<\mathfrak{b}$) and Con($\mathfrak{i}_*<2^{\aleph_0}$). This answers two questions raised in arXiv:1808.02442v3. Besides, we prove the consistency of $\mathfrak{s}_{1/2}^{\infty} < $ non$(\mathcal{E})$ and cov$(\mathcal{E}) < \mathfrak{r}_{1/2}^{\infty}$, where $\mathcal{E}$ is the $σ$-ideal generated by closed sets of measure zero. |
| title | Cardinal invariants related to density |
| topic | Logic 03E17, 03E35 |
| url | https://arxiv.org/abs/2401.09649 |