Lattices in Locally Definable Subgroups of 〈Rn,+〉

Pantelis E. Eleftheriou; Ya’acov Peterzil

doi:10.1215/00294527-2143889

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Home > Journals > Notre Dame J. Formal Logic > Volume 54 > Issue 3-4 > Article

2013 Lattices in Locally Definable Subgroups of

\langleR^{n},+\rangle

Pantelis E. Eleftheriou, Ya’acov Peterzil

Notre Dame J. Formal Logic 54(3-4): 449-461 (2013). DOI: 10.1215/00294527-2143889

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Abstract

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.

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Pantelis E. Eleftheriou. Ya’acov Peterzil. "Lattices in Locally Definable Subgroups of $\langleR^{n},+\rangle$ ." Notre Dame J. Formal Logic 54 (3-4) 449 - 461, 2013. https://doi.org/10.1215/00294527-2143889