Real Algebraic and Analytic Geometry |

Pseudo Completions and Completion in Stages of o-minimal Structures.

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homepage: http://personalpages.manchester.ac.uk/staff/Marcus.Tressl/index.php

Submission: 2006, January 20.

*Abstract:
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.:
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