Long Strong Chains of Subsets of $ω_1$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911601639030784 |
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| author | Asperó, David Gallart, Curial |
| author_facet | Asperó, David Gallart, Curial |
| contents | We force the existence of a chain of length $ω_3$ in $[ω_1]^{ω_1}$ increasing modulo finite. The construction involves symmetric systems of models of two types as side conditions, introduced by the second author. This improves previous results of Koszmider and Veličković-Venturi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15894 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long Strong Chains of Subsets of $ω_1$ Asperó, David Gallart, Curial Logic 03E35, 03E57 We force the existence of a chain of length $ω_3$ in $[ω_1]^{ω_1}$ increasing modulo finite. The construction involves symmetric systems of models of two types as side conditions, introduced by the second author. This improves previous results of Koszmider and Veličković-Venturi. |
| title | Long Strong Chains of Subsets of $ω_1$ |
| topic | Logic 03E35, 03E57 |
| url | https://arxiv.org/abs/2604.15894 |