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On the Existence of Rigid ℵ1-Free Abelian Groups of Cardinality ℵ1

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Abelian Groups and Modules

Part of the book series: Mathematics and Its Applications ((MAIA,volume 343))

Abstract

An abelian group is said to be ℵ1-free if all its countable subgroups are free. A crucial special case of our main result can be stated immediately.

Part of the work for this paper was carried out while the first author visited Rutgers University. He would like to thank the organizers of MAMLS and the Department of Mathematics for their support.

Number of publication 519. Research was supported by the Edmund Landau Center for research in Mathematical Analysis, supported by the Minerva Foundation (Germany)

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Author information

Authors and Affiliations

  1. Fachbereich 6, Universität Essen, 45117, Essen, Germany

    Rüdiger Göbel

  2. Department of Mathematics, Hebrew University, Jerusalem, Israel

    Saharon Shelah

  3. Rutgers University, Newbrunswick, NJ, USA

    Saharon Shelah

Authors
  1. Rüdiger Göbel
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  2. Saharon Shelah
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Informatics, University of Udine, Udine, Italy

    Alberto Facchini

  2. Department of Mathematics, University of Ferrara, Ferrara, Italy

    Claudia Menini

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Göbel, R., Shelah, S. (1995). On the Existence of Rigid ℵ1-Free Abelian Groups of Cardinality ℵ1 . In: Facchini, A., Menini, C. (eds) Abelian Groups and Modules. Mathematics and Its Applications, vol 343. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0443-2_18

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  • DOI: https://doi.org/10.1007/978-94-011-0443-2_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4198-0

  • Online ISBN: 978-94-011-0443-2

  • eBook Packages: Springer Book Archive

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