A descending chain condition for groups definable in o -minimal structures

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Annals of Pure and Applied Logic 134 (2):303-313 (2005)
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Abstract

We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest type-definable subgroup G00 of bounded index and G/G00 equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth author

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10.1016/j.apal.2005.01.002

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Citations of this work

O-Minimal Spectra, Infinitesimal Subgroups and Cohomology.Alessandro Berarducci - 2007 - Journal of Symbolic Logic 72 (4):1177 - 1193.
One-basedness and groups of the form G/G00.Davide Penazzi - 2011 - Archive for Mathematical Logic 50 (7-8):743-758.
Non-standard lattices and o-minimal groups.Pantelis E. Eleftheriou - 2013 - Bulletin of Symbolic Logic 19 (1):56-76.

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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.
One-dimensional groups over an o-minimal structure.Vladimir Razenj - 1991 - Annals of Pure and Applied Logic 53 (3):269-277.
Intersection theory for o-minimal manifolds.Alessandro Berarducci & Margarita Otero - 2001 - Annals of Pure and Applied Logic 107 (1-3):87-119.
Transfer methods for o-minimal topology.Alessandro Berarducci & Margarita Otero - 2003 - Journal of Symbolic Logic 68 (3):785-794.

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