Cardinal invariants associated with the combinatorics of the uniformity number of the ideal of meager-additive sets
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929758519951360 |
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| author | Cardona, Miguel A. |
| author_facet | Cardona, Miguel A. |
| contents | In [CMRM24], it was proved that it is relatively consistent that \emph{bounding number} $\mathfrak{b}$ is smaller than the uniformity of $\mathcal{MA}$, where $\mathcal{MA}$ denotes the ideal of the meager-additive sets of $2^ω$. To establish this result, a specific cardinal invariant, which we refer to as $\mathfrak{b}_b^\mathsf{eq}$, was introduced in close relation to Bartoszyński's and Judah's characterization of the uniformity of $\mathcal{MA}$. This survey aims to explore this cardinal invariant along with its dual, which we call as $\mathfrak{d}_b^\mathsf{eq}$. In particular, we will illustrate its connections with the cardinals represented in Cichoń's diagram. Furthermore, we will present several open problems pertaining to these cardinals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_10514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cardinal invariants associated with the combinatorics of the uniformity number of the ideal of meager-additive sets Cardona, Miguel A. Logic 03E05, 03E17, 03E35, 03E40 In [CMRM24], it was proved that it is relatively consistent that \emph{bounding number} $\mathfrak{b}$ is smaller than the uniformity of $\mathcal{MA}$, where $\mathcal{MA}$ denotes the ideal of the meager-additive sets of $2^ω$. To establish this result, a specific cardinal invariant, which we refer to as $\mathfrak{b}_b^\mathsf{eq}$, was introduced in close relation to Bartoszyński's and Judah's characterization of the uniformity of $\mathcal{MA}$. This survey aims to explore this cardinal invariant along with its dual, which we call as $\mathfrak{d}_b^\mathsf{eq}$. In particular, we will illustrate its connections with the cardinals represented in Cichoń's diagram. Furthermore, we will present several open problems pertaining to these cardinals. |
| title | Cardinal invariants associated with the combinatorics of the uniformity number of the ideal of meager-additive sets |
| topic | Logic 03E05, 03E17, 03E35, 03E40 |
| url | https://arxiv.org/abs/2503.10514 |