## 2007.187: Pseudo completions and completions in stages of o-minimal structures

2007.187:
Marcus Tressl
(2006)
*Pseudo completions and completions in stages of o-minimal structures.*
Archive for Mathematical Logic, 45 (8).
pp. 983-1009.
ISSN 1432-0665

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DOI: 10.1007/s00153-006-0022-2

## 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.

Item Type: | Article |
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Subjects: | MSC 2000 > 03 Mathematical logic and foundations MSC 2000 > 12 Field theory and polynomials MSC 2000 > 13 Commutative rings and algebras |

MIMS number: | 2007.187 |

Deposited By: | Mrs Louise Healey |

Deposited On: | 20 November 2007 |

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