Groups Definable in Ordered Vector Spaces over Ordered Division Rings

Journal of Symbolic Logic 72 (4):1108 - 1140 (2007)
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Abstract

Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a 'definable quotient group' U/L, for some convex V-definable subgroup U of 〈Mⁿ, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L

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Citations of this work

Definable groups in models of Presburger Arithmetic.Alf Onshuus & Mariana Vicaría - 2020 - Annals of Pure and Applied Logic 171 (6):102795.
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.
Intersection theory for o-minimal manifolds.Alessandro Berarducci & Margarita Otero - 2001 - Annals of Pure and Applied Logic 107 (1-3):87-119.

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