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Groups definable in linear o-minimal structures: the non-compact case
Published online by Cambridge University Press: 12 March 2014
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.
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- Copyright © Association for Symbolic Logic 2010
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