A note on adding isomorphisms and the pseudointersection number

2025/10/13 by Switzer, Corey Bacal
#FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.2510.11155

Abstract

We prove that for every tower \mathcal T there are ℵ₁-dense A and B so that any ``reasonable" forcing notion 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 MA_ℵ1(σ\rm -centered) holds in all known models of BA, which provides intrigue to well known questions of Todorčević and Steprāns-Watson.

Citations

• Weak Baumgartner axioms and universal spaces
• Products and countable dense homogeneity

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