Real Algebraic and Analytic Geometry
Submission: 2003, December 15.
The setting of this paper is real closed valued fields. We prove that the value group and the residue field are fully embedded, via a three sorted quantifier elimination. We also investigate the embedding of the algebraic closure as a valued field. Also included is a classification of one types. Finally we study the linear structure induced by the valuation ring, and introduce a collection of sorts G. In a subsequent paper we show that the theory has elimination of imaginaries to the sorts G.
Mathematics Subject Classification (2000): 03C60, 12J10, 12J15, 03C10, 03C45.
Keywords and Phrases: Real Closed Valued Fields, Imaginaries.
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