Maximal eventually different families for uniformly weak Ramsey ideals
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909441247412224 |
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| author | He, Jialiang Luo, Jintao Schrittesser, David Zhang, Hang |
| author_facet | He, Jialiang Luo, Jintao Schrittesser, David Zhang, Hang |
| contents | We study $\mathcal I$-maximal eventually different families of functions from the set of natural numbers into itself where $\mathcal I$ is an arbitrary ideal on the set of natural numbers that includes the ideal of all finite sets $\mathrm{fin}$. We introduce the class of uniformly weak Ramsey ideals and prove that there exists a closed $\mathcal I$-maximal eventually different family if $\mathcal I$ belongs to this class; this is the case for arbitrary $F_σ$ ideals and Fubini products $\mathrm{fin}^α$ with $α<ω_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal eventually different families for uniformly weak Ramsey ideals He, Jialiang Luo, Jintao Schrittesser, David Zhang, Hang Logic 03E15, 03E05 We study $\mathcal I$-maximal eventually different families of functions from the set of natural numbers into itself where $\mathcal I$ is an arbitrary ideal on the set of natural numbers that includes the ideal of all finite sets $\mathrm{fin}$. We introduce the class of uniformly weak Ramsey ideals and prove that there exists a closed $\mathcal I$-maximal eventually different family if $\mathcal I$ belongs to this class; this is the case for arbitrary $F_σ$ ideals and Fubini products $\mathrm{fin}^α$ with $α<ω_1$. |
| title | Maximal eventually different families for uniformly weak Ramsey ideals |
| topic | Logic 03E15, 03E05 |
| url | https://arxiv.org/abs/2412.18987 |