𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Definable group extensions in semi-bounded o-minimal structures

✍ Scribed by Mário J. Edmundo; Pantelis E. Eleftheriou

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
109 KB
Volume
55
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

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) definable group B by 〈R^m^, +〉 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 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.

Uniform bounds on growth in o-minimal st
Uniform bounds on growth in o-minimal structures
✍ Janak Ramakrishnan 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 73 KB

## Abstract We prove that a function definable with parameters in an o‐minimal structure is bounded away from ∞ as its argument goes to ∞ by a function definable without parameters, and that this new function can be chosen independently of the parameters in the original function. This generalizes a

Landolt-börnstein. Numerical data and fu
Landolt-börnstein. Numerical data and functional relationships in science and technology. New Series. Editor in Chief: O. Madelung Group III: Crystal and Solid State Physics. Vol. 14: Supplement and Extension to Vol. III/6 Structure Data of Elements and Intermetallic Phases Subvolume b: Sulfides, Selenides, Tellurides. Part 2: DyErTe … TeZr. By B. Eisenmann H. Schäfer K.-H. Hellwege A. M. Hellwege. Springer-Verlag Berlin 1986. XXIII + 499 pp. Hard cover DM 1280.— ISBN 3-540-16402-2
✍ P. Paufler 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 79 KB