Metric spaces are universal for bi-interpretation with metric structures |
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Institution: | Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Dr., Madison, WI 53706, United States of America |
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Abstract: | In the context of metric structures introduced by Ben Yaacov, Berenstein, Henson, and Usvyatsov 3], 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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Keywords: | Metric structures Continuous logic Bi-interpretation Computable structure theory |
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