Quantifier elimination for the theory of algebraically closed valued fields with analytic structure
✍ Scribed by Yalın F. Çelikler
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 177 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
The theory of algebraically closed non‐Archimedean valued fields is proved to eliminate quantifiers in an analytic language similar to the one used by Cluckers, Lipshitz, and Robinson. The proof makes use of a uniform parameterized normalization theorem which is also proved in this paper. This theorem also has other consequences in the geometry of definable sets. The method of proving quantifier elimination in this paper for an analytic language does not require the algebraic quantifier elimination theorem of Weispfenning, unlike the customary method of proof used in similar earlier analytic quantifier elimination theorems. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)