Archive for Mathematical Logic 45 (8):983-1009 (2006)

Abstract
For an o-minimal expansion R of a real closed field and a set $\fancyscript{V}$ of Th(R)-convex valuation rings, we construct a “pseudo completion” with respect to $\fancyscript{V}$ . This is an elementary extension S of R generated by all completions of all the residue fields of the $V \in \fancyscript{V}$ , 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 $\fancyscript{V} $ . S is the “smallest” extension of R such that all residue fields of the unique extensions of all $V \in \fancyscript{V}$ to S are complete
Keywords Mathematics   Algebra   Mathematics, general   Mathematical Logic and Foundations
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DOI 10.1007/s00153-006-0022-2
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References found in this work BETA

T-Convexity and Tame Extensions.Dries Lou Van Den & H. Lewenberg Adam - 1995 - Journal of Symbolic Logic 60 (1):74 - 102.
Definable Types in o-Minimal Theories.David Marker & Charles I. Steinhorn - 1994 - Journal of Symbolic Logic 59 (1):185-198.
Definable Types in $Mathscr{O}$-Minimal Theories.David Marker & Charles I. Steinhorn - 1994 - Journal of Symbolic Logic 59 (1):185-198.
$T$-Convexity And Tame Extensions.Lou van den Dries & Adam H. Lewenberg - 1995 - Journal of Symbolic Logic 60 (1):74-102.

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Citations of this work BETA

Heirs of Box Types in Polynomially Bounded Structures.Marcus Tressl - 2009 - Journal of Symbolic Logic 74 (4):1225 - 1263.

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