Full Souslin trees at small cardinals
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909123019276288 |
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| author | Rinot, Assaf Yadai, Shira You, Zhixing |
| author_facet | Rinot, Assaf Yadai, Shira You, Zhixing |
| contents | A $κ$-tree is said to be full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $κ$-Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal. Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be $\aleph_3$ many full $\aleph_2$-trees such that the product of any countably many of them is an $\aleph_2$-Souslin tree. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_00299 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Full Souslin trees at small cardinals Rinot, Assaf Yadai, Shira You, Zhixing Logic Primary 03E05. Secondary 03E35 A $κ$-tree is said to be full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $κ$-Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal. Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be $\aleph_3$ many full $\aleph_2$-trees such that the product of any countably many of them is an $\aleph_2$-Souslin tree. |
| title | Full Souslin trees at small cardinals |
| topic | Logic Primary 03E05. Secondary 03E35 |
| url | https://arxiv.org/abs/2308.00299 |