Chains and antichains in the Weihrauch lattice
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911650348531712 |
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| author | Lempp, Steffen Marcone, Alberto Valenti, Manlio |
| author_facet | Lempp, Steffen Marcone, Alberto Valenti, Manlio |
| contents | We study the existence and the distribution of "long" chains in the Weihrauch degrees, mostly focusing on chains with uncountable cofinality. We characterize when such chains have an upper bound and prove that there are no cofinal chains (of any order type) in the Weihrauch degrees. Furthermore, we show that the existence of coinitial sequences of non-zero degrees is equivalent to $\mathrm{CH}$. Finally, we explore the extendibility of antichains, providing some necessary conditions for maximality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chains and antichains in the Weihrauch lattice Lempp, Steffen Marcone, Alberto Valenti, Manlio Logic Primary 03D30, Secondary 03D78 We study the existence and the distribution of "long" chains in the Weihrauch degrees, mostly focusing on chains with uncountable cofinality. We characterize when such chains have an upper bound and prove that there are no cofinal chains (of any order type) in the Weihrauch degrees. Furthermore, we show that the existence of coinitial sequences of non-zero degrees is equivalent to $\mathrm{CH}$. Finally, we explore the extendibility of antichains, providing some necessary conditions for maximality. |
| title | Chains and antichains in the Weihrauch lattice |
| topic | Logic Primary 03D30, Secondary 03D78 |
| url | https://arxiv.org/abs/2411.07792 |