Universality of group embeddability

Universality of group embeddability
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群体嵌入性的普遍性

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发表时间：
2017
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通讯作者：
L. Ros
L. Ros
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文献类型：
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作者：
F. Calderoni;L. Ros

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在Borel可约性的框架下，我们研究了群之间可嵌入性的各种概念。我们证明了可数群之间的可嵌入性、(离散)Polish群之间的拓扑可嵌性以及具有有界双不变完备度量的可分群之间的等距可嵌入性都是不变的泛解析拟序。这加强了[Wil14]和[FLR09]的一些结果。
Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the isometric embeddability between separable groups with a bounded bi-invariant complete metric are all invariantly universal analytic quasi-orders. This strengthens some results from [Wil14] and [FLR09].