0-D-Valued Fields

Journal of Symbolic Logic 71 (2):639 - 660 (2006)

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
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DOI 10.2178/jsl/1146620164
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