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Ax-Kochen-Ershov Principles for Valued and Ordered Vector Spaces

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Ordered Algebraic Structures

Abstract

We study extensions of valued vector spaces with variable base field, introducing the notion of disjointness and valuation disjointness in this setting. We apply the results to determine the model theoretic properties of valued vector spaces (with variable base field) relative to that of their skeletons. We study the model theory of the skeletons in special cases. We apply the results to ordered vector spaces with compatible valuation.

1This paper was written while the second author was supported by the Deutsche Forschungsgemeinschaft. This paper represents some results from the second author’s doctoral thesis.

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References

  1. C.C. Chang & H. J. Keisler, Model Theory. Amsterdam (1973).

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  2. L. van den Dries, Quantifier elimination for linear formulas over ordered and valued fields. Bull. Soc. Math. Belg. 23 (1981), 19–32.

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  5. S. Kuhlmann, Valuation bases for extensions of valued vector spaces. To appear in Forum Math (1995).

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  6. S. Kuhlmann, Infinitary properties of valued and ordered vector spaces. Submitted.

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  7. F.-V. Kuhlmann, Valuation theory of fields, Abelian groups and modules. To appear in the “Algebra, Logic & Applications” series, eds. Göbel & Macintyre, Gordon & Breach, New York.

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Authors
  1. Franz-Viktor Kuhlmann
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  2. Salma Kuhlmann
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Bowling Green State University, Bowling Green, Ohio, USA

    W. Charles Holland

  2. Caribbean Mathematics Foundation, Department of Mathematics, University of Florida, Gainesville, Florida, USA

    Jorge Martinez

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© 1997 Springer Science+Business Media Dordrecht

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Kuhlmann, FV., Kuhlmann, S. (1997). Ax-Kochen-Ershov Principles for Valued and Ordered Vector Spaces. In: Holland, W.C., Martinez, J. (eds) Ordered Algebraic Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5640-0_10

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  • DOI: https://doi.org/10.1007/978-94-011-5640-0_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6378-4

  • Online ISBN: 978-94-011-5640-0

  • eBook Packages: Springer Book Archive

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