Tressl, Marcus (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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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 V epsilon 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 V epsilon V to S are complete.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 19 Jan 2021 09:45 |
| Last Modified: | 19 Jan 2021 09:45 |
| URI: | https://pred.uni-regensburg.de/id/eprint/33788 |
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