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Groups definable in ordered vector spaces over ordered division rings

Published online by Cambridge University Press:  12 March 2014

Pantelis E. Eleftheriou  and
Sergei Starchenko
Pantelis E. Eleftheriou
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, In 46556., USA. E-mail: pelefthe@nd.edu
Sergei Starchenko
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, In 46556., USA. E-mail: starchenko.l@nd.edu
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Abstract

Let M = 〈M, +, <, 0, {λ}λЄD〉 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.

Keywords

O-minimal structuresdefinably compact groupsquotient by lattice
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 4 , December 2007 , pp. 1108 - 1140
Copyright
Copyright © Association for Symbolic Logic 2007

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