Filtration-equivalent א1-separable abelian groups of cardinality א1

Saharon Shelah; Lutz Strüngmann

doi:10.1016/j.apal.2009.12.001

Filtration-equivalent א₁-separable abelian groups of cardinality א₁

Saharon Shelah
, Lutz Strüngmann^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that it is consistent with ordinary set theory Z F C and the generalized continuum hypothesis that there exist two א₁-separable abelian groups of cardinality א₁ which are filtration-equivalent and one is a Whitehead group but the other is not. This solves one of the open problems from Eklof and Mekler (2002) [2].

Original language	English
Pages (from-to)	935-943
Number of pages	9
Journal	Annals of Pure and Applied Logic
Volume	161
Issue number	7
DOIs	https://doi.org/10.1016/j.apal.2009.12.001
State	Published - Apr 2010

Keywords

Filtration equivalent groups
Whitehead groups
א-separable groups

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10.1016/j.apal.2009.12.001

Cite this

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title = "Filtration-equivalent א1-separable abelian groups of cardinality א1",

abstract = "We show that it is consistent with ordinary set theory Z F C and the generalized continuum hypothesis that there exist two א1-separable abelian groups of cardinality א1 which are filtration-equivalent and one is a Whitehead group but the other is not. This solves one of the open problems from Eklof and Mekler (2002) [2].",

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AB - We show that it is consistent with ordinary set theory Z F C and the generalized continuum hypothesis that there exist two א1-separable abelian groups of cardinality א1 which are filtration-equivalent and one is a Whitehead group but the other is not. This solves one of the open problems from Eklof and Mekler (2002) [2].

KW - Filtration equivalent groups

KW - Whitehead groups

KW - א-separable groups

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IS - 7

ER -

Filtration-equivalent א₁-separable abelian groups of cardinality א₁

Abstract

Keywords

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