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Groups definable in linear o-minimal structures: the non-compact case

Published online by Cambridge University Press:  12 March 2014

Pantelis E. Eleftheriou
Pantelis E. Eleftheriou*
Affiliation:
CMAF, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal, E-mail: pelefthe@gmail.com
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Abstract

Let = ⟨M, +, <, 0, S⟩ be a linear o-minimal expansion of an ordered group, and G = ⟨G, ⊕,eG) an n-dimensional group definable in . We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L. for some convex ∨-definable subgroup U of ⟨Mn, +⟩ and a lattice L of rank equal to the dimension of the ‘compact part’ of G.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 1 , March 2010 , pp. 208 - 220
Copyright
Copyright © Association for Symbolic Logic 2010

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