Journal of Mathematical Logic 20 (2):2050009 (2019)

Abstract
We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. 18 885–903]. Let [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same result holds when [Formula: see text] is definable in any o-minimal expansion of [Formula: see text] which is elementarily equivalent to [Formula: see text]. We observe that the above statement is equivalent to saying: there exists an [Formula: see text] such that [Formula: see text] is an approximate subgroup of [Formula: see text].
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DOI 10.1142/s0219061320500099
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Locally Definable Homotopy.Elías Baro & Margarita Otero - 2010 - Annals of Pure and Applied Logic 161 (4):488-503.
Locally Definable Homotopy.Elías Baro & Marg\ Otero - 2010 - Annals of Pure and Applied Logic 161 (4):488-503.

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