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Definable quotients of locally definable groups. (English) Zbl 1273.03130
Summary: We study locally definable abelian groups \({\mathcal{U}}\) in various settings and examine conditions under which the quotient of \({\mathcal{U}}\) by a discrete subgroup might be definable. This turns out to be related to the existence of the type-definable subgroup \({\mathcal{U}^{00}}\) and to the divisibility of \({\mathcal{U}}\).

MSC:
03C64 Model theory of ordered structures; o-minimality
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
20A15 Applications of logic to group theory
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