Journal of Symbolic Logic

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

Pantelis E. Eleftheriou

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Let ℳ=〈 M, +, <, 0, S〉 be a linear o-minimal expansion of an ordered group, and G=〈 G, ⊕, eG〉 an n-dimensional group definable in ℳ. 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.

Article information

J. Symbolic Logic, Volume 75, Issue 1 (2010), 208-220.

First available in Project Euclid: 25 January 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C64: Model theory of ordered structures; o-minimality 46A40: Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]

O-minimal structures Quotient by lattice


Eleftheriou, Pantelis E. Groups definable in linear o-minimal structures: the non-compact case. J. Symbolic Logic 75 (2010), no. 1, 208--220. doi:10.2178/jsl/1264433916.

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