Metric Spaces Are Universal for Biinterpretation with Metric Structures
Abstract
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 biinterpretation 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.14957
 Bibcode:
 2021arXiv210314957H
 Keywords:

 Mathematics  Logic;
 03C66;
 03C57
 EPrint:
 21 pages