0-D-valued fields

In [Sca99], 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.

• Type: Journal
• Year: 2006
• Where: JSYML
• Authors: Nicolas Guzy
• Keywords: Analogous Theorem, Angular Component Functions, JSYML 2006, Three-sorted Language