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Lattices in locally definable subgroups of \(\langle R^{n},+\rangle\). (English) Zbl 1345.03072
Summary: Let \(\mathcal{M}\) be an o-minimal expansion of a real closed field \(R\). We define the notion of a lattice in a locally definable group and then prove that every connected, definably generated subgroup of \(\langle R^{n},+\rangle\) contains a definable generic set and therefore admits a lattice.

03C64 Model theory of ordered structures; o-minimality
03C68 Other classical first-order model theory
22B99 Locally compact abelian groups (LCA groups)
Full Text: DOI Euclid
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