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December 2007 Groups definable in ordered vector spaces over ordered division rings
Pantelis E. Eleftheriou, Sergei Starchenko
J. Symbolic Logic 72(4): 1108-1140 (December 2007). DOI: 10.2178/jsl/1203350776

Abstract

Let $\mathcal{M} = \langle M, +, <, 0, \{\lambda\}_{\lambda \in D}\rangle$ be an ordered vector space over an ordered division ring $D$, and $G = \langle G, \oplus, e_G \rangle$ an $n$-dimensional group definable in $\mathcal{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 $\bigvee$-definable subgroup $U$ of $\langle M^n, + \rangle$ and a lattice $L$ of rank $n$. As two consequences, we derive Pillay’s conjecture for a saturated $\mathcal{M}$ as above and we show that the o-minimal fundamental group of $G$ is isomorphic to $L$.

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Pantelis E. Eleftheriou. Sergei Starchenko. "Groups definable in ordered vector spaces over ordered division rings." J. Symbolic Logic 72 (4) 1108 - 1140, December 2007. https://doi.org/10.2178/jsl/1203350776

Information

Published: December 2007
First available in Project Euclid: 18 February 2008

zbMATH: 1130.03028
MathSciNet: MR2371195
Digital Object Identifier: 10.2178/jsl/1203350776

Subjects:
Primary: 03C64 , 22C05 , 46A40

Keywords: definably compact groups , o-minimal structures , quotient by lattice

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 4 • December 2007
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