Definable group extensions in semi‐bounded o‐minimal structures

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

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, +〉
Keywords group extensions  O‐minimal structures
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DOI 10.1002/malq.200910027
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References found in this work BETA

Definably Compact Abelian Groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
Type-Definability, Compact Lie Groups, and o-Minimality.Anand Pillay - 2004 - Journal of Mathematical Logic 4 (02):147-162.
One-Dimensional Groups Over an o-Minimal Structure.Vladimir Razenj - 1991 - Annals of Pure and Applied Logic 53 (3):269-277.
A Structure Theorem for Semibounded Sets in the Reals.Ya'acov Peterzil - 1992 - Journal of Symbolic Logic 57 (3):779-794.

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Coverings by Open Cells.Mário J. Edmundo, Pantelis E. Eleftheriou & Luca Prelli - 2014 - Archive for Mathematical Logic 53 (3-4):307-325.

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