Filtration equivalent aleph₁-separable abelian groups of cardinality aleph₁

2006/12/09 by Saharon Shelah, Shelah, Saharon, Lutz Strüngmann +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO

paper · pdf · doi:10.48550/arxiv.math/0612241

published as Ann. Pure Appl. Logic 161 No. 7 (2010) 935--943

arxiv created 2006/12/09 · openalex publication_date 2006/12/09 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that it is consistent with ordinary set theory ZFC and the generalized continuum hypothesis that there exist two separable abelian groups of cardinality aleph₁ which are filtration equivalent and one is a Whitehead group but the other is not. This solves one of the open problems of Eklof and Mekler.

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