Real Algebraic and Analytic Geometry

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74. Timothy Mellor:
Imaginaries in Real Closed Valued Fields I.


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.

Full text, 41p.: dvi 162k, ps.gz 215k, pdf 329k.

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