Real Algebraic and Analytic Geometry
Submission: 2006, January 20.
For an o-minimal expansion R of a real closed field and a set V of Th(R)-convex valuation rings, we construct a ``pseudo completion'' with respect to V. This is an elementary extension S of R generated by all completions of all the residue fields of the A from V, when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings up to an R-isomorphism. For polynomially bounded R we can iterate the construction of the pseudo completion in order to get a ``completion in stages" S of R with respect to V. S is the ``smallest" extension of R such that all residue fields of the unique extensions of all A from V to S are complete.
Mathematics Subject Classification (2000): 03C64, 12J10, 12J15, 13B35.
Keywords and Phrases: valuation, real closed field, o-minimal structure, completion.
Full text, 23p.: dvi 139k, ps.gz 199k, pdf 268k.