Adding cofinal countable sequences through multiple regular cardinals by ssp forcing
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911237039718400 |
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| author | De Bondt, Ben Velickovic, Boban |
| author_facet | De Bondt, Ben Velickovic, Boban |
| contents | We present a direct construction of stationary set preserving forcings that make $ω$-cofinal all the members of some arbitrary set $\mathcal{K}$ of regular cardinals $κ> ω_1$. In addition, it is made possible to ensure that no other uncountable regular cardinals from the ground model acquire countable cofinality in the forcing extension. Our method is elementary, being based on a combinatorial argument by Foreman and Magidor together with generalizations of typical side-condition arguments and needs no assumptions beyond $\mathsf{ZFC}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24634 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adding cofinal countable sequences through multiple regular cardinals by ssp forcing De Bondt, Ben Velickovic, Boban Logic 03E40, 03E10 We present a direct construction of stationary set preserving forcings that make $ω$-cofinal all the members of some arbitrary set $\mathcal{K}$ of regular cardinals $κ> ω_1$. In addition, it is made possible to ensure that no other uncountable regular cardinals from the ground model acquire countable cofinality in the forcing extension. Our method is elementary, being based on a combinatorial argument by Foreman and Magidor together with generalizations of typical side-condition arguments and needs no assumptions beyond $\mathsf{ZFC}$. |
| title | Adding cofinal countable sequences through multiple regular cardinals by ssp forcing |
| topic | Logic 03E40, 03E10 |
| url | https://arxiv.org/abs/2510.24634 |