Some Banach spaces added by a Cohen real

2014/09/29 by Mirna Džamonja, Džamonja, Mirna
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1409.8172

openalex publication_date 2014/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study certain Banach spaces that are added in the extension by one Cohen real. Specifically, we show that adding just one Cohen real to any model adds a Banach space of density ℵ₁ which does not embed into any such space in the ground model such a Banach space can be chosen to be UG This has consequences on the the isomorphic universality number for Banach spaces of density ℵ₁, which is hence equal to ℵ₂ in the standard Cohen model and the same is true for UG spaces. Analogous universality results for Banach spaces are true for other cardinals, by a different proof.

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