Groups definable in two orthogonal sorts

Alessandro Berarducci; Marcello Mamino

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arXiv · 1304.1380

Groups definable in two orthogonal sorts

Alessandro Berarducci·Marcello Mamino

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Abstract

This work can be thought as a contribution to the model theory of group extensions. We study the groups G which are interpretable in the disjoint union of two structures (seen as a two-sorted structure). We show that if one of the two structures is superstable of finite Lascar rank and the Lascar rank is definable, then G is an extension of a group internal to the (possibly) unstable sort by a definable subgroup internal to the stable sort. In the final part of the paper we show that if the unstable sort is an o-minimal expansion of the reals, then G has a natural Lie structure and the extension is a topological cover.

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BibTeX RIS

Alessandro Berarducci, Marcello Mamino. 2013-04-04. Groups definable in two orthogonal sorts. https://arxiv.org/abs/1304.1380

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