Journal of Symbolic Logic

0-D-valued fields

Nicolas Guzy

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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 ℒ₂ 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.

Article information

Source
J. Symbolic Logic, Volume 71, Issue 2 (2006), 639-660.

Dates
First available in Project Euclid: 2 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1146620164

Digital Object Identifier
doi:10.2178/jsl/1146620164

Mathematical Reviews number (MathSciNet)
MR2225899

Zentralblatt MATH identifier
1109.03029

Subjects
Primary: 03C10: Quantifier elimination, model completeness and related topics 12H05: Differential algebra [See also 13Nxx] 12J10: Valued fields

Keywords
Valued D-fields quantifier elimination real-series closed fields positivstellensatz

Citation

Guzy, Nicolas. 0-D-valued fields. J. Symbolic Logic 71 (2006), no. 2, 639--660. doi:10.2178/jsl/1146620164. https://projecteuclid.org/euclid.jsl/1146620164


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References

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