Cardinal characteristics associated with small subsets of reals
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929711200862208 |
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| author | Cardona, Miguel A. Marton, Adam Supina, Jaroslav |
| author_facet | Cardona, Miguel A. Marton, Adam Supina, Jaroslav |
| contents | Inspired by Bartoszyński's work on small sets, we introduce a new ideal defined by interval partitions on natural numbers and summable sequences of positive reals. Similarly, we present another ideal that relies on Bartoszyński's and Shelah's representation of $F_σ$ measure zero sets. We show they are $σ$-ideals characterizing all small sets and $F_σ$ measure zero sets. We also study the cardinal characteristics associated with the introduced ideals. We use them to describe the invariants of measure, discuss their connection to Cichoń's diagram, and present related consistency results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cardinal characteristics associated with small subsets of reals Cardona, Miguel A. Marton, Adam Supina, Jaroslav Logic Inspired by Bartoszyński's work on small sets, we introduce a new ideal defined by interval partitions on natural numbers and summable sequences of positive reals. Similarly, we present another ideal that relies on Bartoszyński's and Shelah's representation of $F_σ$ measure zero sets. We show they are $σ$-ideals characterizing all small sets and $F_σ$ measure zero sets. We also study the cardinal characteristics associated with the introduced ideals. We use them to describe the invariants of measure, discuss their connection to Cichoń's diagram, and present related consistency results. |
| title | Cardinal characteristics associated with small subsets of reals |
| topic | Logic |
| url | https://arxiv.org/abs/2405.11312 |