Generalized Tukey reducibility between $σ$-directed sets
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866913935072952320 |
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| author | Sakai, Hiroshi Tanno, Toshimasa |
| author_facet | Sakai, Hiroshi Tanno, Toshimasa |
| contents | We introduce the pre-Tukey reducibility, a generalization of the Tukey reducibility between directed sets that works well in $\mathsf{ZF}$. We investigate the pre-Tukey reducibility between several $σ$-directed sets under assumptions on sets of reals, which hold in the Solovay model and in $L(\mathbb{R})$ satisfying $\mathsf{AD}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Tukey reducibility between $σ$-directed sets Sakai, Hiroshi Tanno, Toshimasa Logic We introduce the pre-Tukey reducibility, a generalization of the Tukey reducibility between directed sets that works well in $\mathsf{ZF}$. We investigate the pre-Tukey reducibility between several $σ$-directed sets under assumptions on sets of reals, which hold in the Solovay model and in $L(\mathbb{R})$ satisfying $\mathsf{AD}$. |
| title | Generalized Tukey reducibility between $σ$-directed sets |
| topic | Logic |
| url | https://arxiv.org/abs/2507.07309 |