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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2402.00144 |
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| _version_ | 1866914903070081024 |
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| author | Cardona, Miguel A. |
| author_facet | Cardona, Miguel A. |
| contents | We have revised the softness property introduced by Jörg Brendle and Haim Judah (perfect sets of random reals. Israel J. Math., 83(1-2):153-176, 1993), to present a new definition of a class of posets called $σ$-soft-linked. Our work demonstrates that these posets work well to preserve the evasion number as well as the bounding number small in generic extensions. Furthermore, we establish a connection between our concept and the Fréchet-linked notion introduced by Diego A. Mejía (Matrix iterations with vertical support restrictions. In Proceedings of the 14th1 and 15th Asian Logic Conferences, pages 213-248. World Sci. Publ., Hackensack, NJ, 2019). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Soft-linkedness Cardona, Miguel A. Logic Combinatorics 03E05, 03E17, 03E35, 03E40 We have revised the softness property introduced by Jörg Brendle and Haim Judah (perfect sets of random reals. Israel J. Math., 83(1-2):153-176, 1993), to present a new definition of a class of posets called $σ$-soft-linked. Our work demonstrates that these posets work well to preserve the evasion number as well as the bounding number small in generic extensions. Furthermore, we establish a connection between our concept and the Fréchet-linked notion introduced by Diego A. Mejía (Matrix iterations with vertical support restrictions. In Proceedings of the 14th1 and 15th Asian Logic Conferences, pages 213-248. World Sci. Publ., Hackensack, NJ, 2019). |
| title | Soft-linkedness |
| topic | Logic Combinatorics 03E05, 03E17, 03E35, 03E40 |
| url | https://arxiv.org/abs/2402.00144 |