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arXiv · 2510.11155

A note on adding isomorphisms and the pseudointersection number

Corey Bacal Switzer
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Abstract

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 $\mathsf{MA}_{\aleph_1}(\sigma{\rm -centered})$ holds in all known models of $\mathsf{BA}$, which provides intrigue to well known questions of Todor\v{c}evi\'c and Stepr\=ans-Watson.

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Corey Bacal Switzer. 2025-10-13. A note on adding isomorphisms and the pseudointersection number. https://arxiv.org/abs/2510.11155

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