Hindman's Theorem in the hierarchy of Choice Principles
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916109125419008 |
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| author | Fernández-Bretón, David J. |
| author_facet | Fernández-Bretón, David J. |
| contents | In the context of $\mathsf{ZF}$, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the $\mathsf{AC}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_06156 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hindman's Theorem in the hierarchy of Choice Principles Fernández-Bretón, David J. Logic Primary 03E25, Secondary 03E35, 03E30, 03E65, 03E02, 03E05 In the context of $\mathsf{ZF}$, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the $\mathsf{AC}$. |
| title | Hindman's Theorem in the hierarchy of Choice Principles |
| topic | Logic Primary 03E25, Secondary 03E35, 03E30, 03E65, 03E02, 03E05 |
| url | https://arxiv.org/abs/2203.06156 |