A note on adding isomorphisms and the pseudointersection number
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918159567552512 |
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| author | Switzer, Corey Bacal |
| author_facet | Switzer, Corey Bacal |
| contents | We prove that for every tower $\mathcal T$ there are $\aleph_1$-dense $A$ and $B$ so that any ``reasonable" forcing notion $\mathbb{P}$ -- an adjective that includes all known ones -- for making $A$ and $B$ isomorphic will add a pseudointersection for the tower. This shows in particular that $\mathsf{MA}_{\aleph_1}(σ{\rm -centered})$ holds in all known models of $\mathsf{BA}$, which provides intrigue to well known questions of Todorčević and Steprāns-Watson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on adding isomorphisms and the pseudointersection number Switzer, Corey Bacal Logic General Topology We prove that for every tower $\mathcal T$ there are $\aleph_1$-dense $A$ and $B$ so that any ``reasonable" forcing notion $\mathbb{P}$ -- an adjective that includes all known ones -- for making $A$ and $B$ isomorphic will add a pseudointersection for the tower. This shows in particular that $\mathsf{MA}_{\aleph_1}(σ{\rm -centered})$ holds in all known models of $\mathsf{BA}$, which provides intrigue to well known questions of Todorčević and Steprāns-Watson. |
| title | A note on adding isomorphisms and the pseudointersection number |
| topic | Logic General Topology |
| url | https://arxiv.org/abs/2510.11155 |