Definable group extensions in semi‐bounded o‐minimal structures

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Mathematical Logic Quarterly 55 (6):598-604 (2009)
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Abstract

In this note we show: Let R = 〈R, <, +, 0, …〉 be a semi-bounded o-minimal expansion of an ordered group, and G a group definable in R of linear dimension m . Then G is a definable extension of a bounded definable group B by 〈Rm, +〉

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10.1002/malq.200910027

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Citations of this work

Coverings by open cells.Mário J. Edmundo, Pantelis E. Eleftheriou & Luca Prelli - 2014 - Archive for Mathematical Logic 53 (3-4):307-325.
A semi-linear group which is not affine.Pantelis E. Eleftheriou - 2008 - Annals of Pure and Applied Logic 156 (2):287-289.

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References found in this work

Type-definability, compact lie groups, and o-minimality.Anand Pillay - 2004 - Journal of Mathematical Logic 4 (02):147-162.
Definably compact Abelian groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
A structure theorem for semibounded sets in the reals.Ya'acov Peterzil - 1992 - Journal of Symbolic Logic 57 (3):779-794.
Structure theorems for o-minimal expansions of groups.Mario J. Edmundo - 2000 - Annals of Pure and Applied Logic 102 (1-2):159-181.

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