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Rings of analytic functions definable in o-minimal structure

✍ Scribed by M. Fujita; M. Shiota

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
370 KB
Volume
182
Category
Article
ISSN
0022-4049

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✦ Synopsis

From the ring theoretical viewpoint, especially from the viewpoint of Real Algebra, we consider the ring of analytic functions deÿnable in a given o-minimal expansion of the real ÿeld on a deÿnable real analytic manifold. We ÿnd necessary conditions for o-minimal structures that Artin-Lang property, Real Nullstellensatz and Hilbert 17th Problem for this ring hold true in the three-dimensional case. We also prove that this ring is Noetherian in the three-dimensional case when the given o-minimal structure is the restricted analytic ÿeld.

📜 SIMILAR VOLUMES

Linear Groups Definable in o-Minimal Str
Linear Groups Definable in o-Minimal Structures
✍ Y. Peterzil; A. Pillay; S. Starchenko 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 156 KB

We study subgroups G of GL n, R definable in o-minimal expansions M s Ž . Ž. R, q, и , . . . of a real closed field R. We prove several results such as: a G can be defined using just the field structure on R together with, if necessary, power Ž . functions, or an exponential function definable in M.

Definable group extensions in semi-bound
Definable group extensions in semi-bounded o-minimal structures
✍ Mário J. Edmundo; Pantelis E. Eleftheriou 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 109 KB

## Abstract In this note we show: Let __R__ = 〈__R__, <, +, 0, …〉 be a semi‐bounded (respectively, linear) o‐minimal expansion of an ordered group, and __G__ a group definable in __R__ of linear dimension __m__ ([2]). Then __G__ is a definable extension of a bounded (respectively, definably compact