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0-D-valued fields

Published online by Cambridge University Press:  12 March 2014

Nicolas Guzy
Nicolas Guzy*
Affiliation:
Université de Mons-Hainaut, Le Pentagone, Institut de Mathématique, 6. Avenue du Champ de Mars, B-7000 Mons, Belgium. E-mail: Nicolas.Guzy@umh.ac.be
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Abstract

In [12]. T. Scanlon proved a quantifier elimination result for valued D-fields in a three-sorted language by using angular component functions. Here we prove an analogous theorem in a different language which was introduced by F. Delon in her thesis. This language allows us to lift the quantifier elimination result to a one-sorted language by a process described in the Appendix. As a byproduct, we state and prove a “positivstellensatz” theorem for the differential analogue of the theory of real-series closed fields in the valued D-field setting.

Keywords

Valued D fieldsquantifier eliminationreal-series closed fieldspositivstellensatz
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 2 , June 2006 , pp. 639 - 660
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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