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Strong theories of ordered Abelian groups

Volume 236 / 2017

Alfred Dolich, John Goodrick Fundamenta Mathematicae 236 (2017), 269-296 MSC: Primary 03C45; Secondary 03C64. DOI: 10.4064/fm256-5-2016 Published online: 14 October 2016


We consider strong expansions of the theory of ordered Abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of definable sets in such theories, in particular as relates to definable infinite discrete sets. We also provide a range of examples of strong expansions of ordered Abelian groups which demonstrate the great variety of such theories.


  • Alfred DolichDepartment of Mathematics
    and Computer Science
    Kingsborough Community College Brooklyn, NY, U.S.A.
    Department of Mathematics
    The CUNY Graduate Center New York, NY, U.S.A.
  • John GoodrickDepartamento de Matemáticas
    Universidad de los Andes
    Carrera 1 no. 18A-12
    Bogotá, Colombia

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