Abstract
This work can be thought of 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 normal 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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Partially supported by PRIN 2009WY32E8_003 “O-minimalità, teoria degli insiemi, metodi e modelli non standard e applicazioni”.
Partially supported by Fundação para a Ciência e a Tecnologia grant SFRH/BPD/73859/2010. We also acknowledge the support of FIRB2010, “New advances in the Model Theory of exponentiation”.
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Berarducci, A., Mamino, M. Groups definable in two orthogonal sorts. Isr. J. Math. 208, 413–441 (2015). https://doi.org/10.1007/s11856-015-1205-5
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DOI: https://doi.org/10.1007/s11856-015-1205-5