Adding ℵ_ω many Cohen reals

2025/11/24 by Pedro Marun, Saharon Shelah, Marun, Pedro +3
Computer Science · Mathematics · #03E40 #03E50 #Advanced Algebra and Logic #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2511.19721

openalex publication_date 2025/11/24 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28

Abstract

Abstractly, the generic extensions after ℵ_ω-many Cohen reals and ℵ_ω+1-many Cohen reals must be different for reasons of uniform density the relevant Boolean algebras. Nevertheless this is not satisfying and it would be nice to pin the difference between the two models down to some mathematical or combinatorial principle. In this paper we provide such a principle.

Citations

• Adding a lot of Cohen reals by adding a few

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