度量空间对具有度量结构的双解释是普适的
Metric Spaces Are Universal for Bi-interpretation with Metric Structures
摘要：
在Ben Yaacov，Berenstein，Henson和Usvyatsov提出的度量结构的背景下，我们将可数签名中的度量结构显式编码为空签名中的纯度量空间，表明这种结构对于正直径度量结构的双解释是普适的.这类似于对有限签名中任意离散结构的经典编码，但在某些方面更强，在其他方面更弱。在离散设置中也存在某些细粒度拓扑问题，没有类似物。
英文摘要：
In the context of metric structures introduced by Ben Yaacov, Berenstein, Henson, and Usvyatsov, we exhibit an explicit encoding of metric structures in countable signatures as pure metric spaces in the empty signature, showing that such structures are universal for bi-interpretation among metric structures with positive diameter. This is analogous to the classical encoding of arbitrary discrete structures in finite signatures as graphs, but is stronger in certain ways and weaker in others. There are also certain fine grained topological concerns with no analog in the discrete setting.
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