Groups definable in two orthogonal sorts
Groups definable in two orthogonal sorts
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可按两种正交排序定义的组
DOI：
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发表时间：
2013
影响因子：
1
通讯作者：
M. Mamino
中科院分区：
文献类型：
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作者：
A. Berarducci;M. Mamino
这项工作可以被认为是一个贡献的模型理论的组扩展。我们研究了在两个结构的不交并中可解释的群G（被视为两个排序结构）。我们证明了如果两个结构中的一个是有限Lascar秩的超稳定的，并且Lascar秩是可定义的，则G是（可能）不稳定排序内部的群通过稳定排序内部的可定义正规子群的扩张.在本文的最后一部分，我们证明了，如果不稳定排序是一个o-最小的实数扩展，那么G有一个自然的李结构和扩展是一个拓扑覆盖。
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.