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Model- and substructure complete theories of ordered Abelian groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 1103)

Abstract

We give necessary conditions for an arbitrary elementary class of ordered abelian groups to be model-complete, resp. substructure-complete. Ordered abelian groups are considered in a suitable definitional extension of the usual language of ordered groups. We introduce also the concepts of convex model-completeness and convex substructure completeness.

Keywords

  • Abelian Group
  • Relation Symbol
  • Elementary Class
  • Unary Predicate
  • Definitional Extension

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© 1984 Springer-Verlag

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Schmitt, P.H. (1984). Model- and substructure complete theories of ordered Abelian groups. In: Müller, G.H., Richter, M.M. (eds) Models and Sets. Lecture Notes in Mathematics, vol 1103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099396

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  • DOI: https://doi.org/10.1007/BFb0099396

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13900-3

  • Online ISBN: 978-3-540-39115-9

  • eBook Packages: Springer Book Archive