Many subalgebras of $\mathcal{P}(ω)/\mathit{fin}$
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913005793443840 |
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| author | Hart, Klaas Pieter |
| author_facet | Hart, Klaas Pieter |
| contents | In answer to a question on Mathoverflow we show that the Boolean algebra $\mathcal{P}(ω)/\mathit{fin}$ contains a family $\{\mathcal{B}_X:X\subseteq\mathfrak{c}\}$ of subalgebras with the property that $X\subseteq Y$ implies $\mathcal{B}_Y$ is a subalgebra of $\mathcal{B}_X$ and if $X\not\subseteq Y$ then $\mathcal{B}_Y$ is not embeddable into~$\mathcal{B}_X$. The proof proceeds by Stone duality and the construction of a suitable family of separable zero-dimensional compact spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08491 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Many subalgebras of $\mathcal{P}(ω)/\mathit{fin}$ Hart, Klaas Pieter General Topology Logic Primary 06E05, Secondary: 06E15, 54C05, 54D65, 54G20 In answer to a question on Mathoverflow we show that the Boolean algebra $\mathcal{P}(ω)/\mathit{fin}$ contains a family $\{\mathcal{B}_X:X\subseteq\mathfrak{c}\}$ of subalgebras with the property that $X\subseteq Y$ implies $\mathcal{B}_Y$ is a subalgebra of $\mathcal{B}_X$ and if $X\not\subseteq Y$ then $\mathcal{B}_Y$ is not embeddable into~$\mathcal{B}_X$. The proof proceeds by Stone duality and the construction of a suitable family of separable zero-dimensional compact spaces. |
| title | Many subalgebras of $\mathcal{P}(ω)/\mathit{fin}$ |
| topic | General Topology Logic Primary 06E05, Secondary: 06E15, 54C05, 54D65, 54G20 |
| url | https://arxiv.org/abs/2303.08491 |