A descending chain condition for groups definable in o -minimal structures
Annals of Pure and Applied Logic 134 (2):303-313 (2005)
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 authorAuthor's Profile
DOI
10.1016/j.apal.2005.01.002
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Citations of this work
Groups Definable in Ordered Vector Spaces over Ordered Division Rings.Pantelis E. Eleftheriou & Sergei Starchenko - 2007 - Journal of Symbolic Logic 72 (4):1108 - 1140.
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Compact domination for groups definable in linear o-minimal structures.Pantelis E. Eleftheriou - 2009 - Archive for Mathematical Logic 48 (7):607-623.
One-basedness and groups of the form G/G 00.Davide Penazzi - 2011 - Archive for Mathematical Logic 50 (7-8):743-758.
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References found in this work
Hyperimaginaries and Automorphism Groups.D. Lascar & A. Pillay - 2001 - Journal of Symbolic Logic 66 (1):127-143.
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.
