Filtration equivalent aleph_1-separable abelian groups of cardinality aleph_1

Lutz Str\"ungmann; Saharon Shelah

arxiv: math/0612241 · v1 · pith:TAJ5GPSZnew · submitted 2006-12-09 · 🧮 math.LO

Filtration equivalent aleph₁-separable abelian groups of cardinality aleph₁

Saharon Shelah , Lutz Str\"ungmann This is my paper

classification 🧮 math.LO

keywords alephabeliancardinalityequivalentfiltrationgroupsseparableconsistent

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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 aleph_1 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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Filtration equivalent aleph₁-separable abelian groups of cardinality aleph₁

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