Abstract
There exists a universal object in the class of left-computably enumerable (left-c.e.) metric spaces with diameter bounded by a constant under effective isometric embeddings. There is no such universal object in the class of all left-c.e. metric spaces.
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References
E. Ianovski, R. Miller, S. Ng, and A. Nies, “Complexity of equivalence relations and preorders from computability theory,” J. Symbolic Logic (in press).
A. G. Melnikov and A. Nies, Proceedings of the American Mathematical Society 141(8), 2885 (2013).
A. G. Melnikov and A. Nies, in Proceedings of CiE (Springer, Berlin, 2013), pp. 320–328.
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Submitted by M. M. Arslanov
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Gavruskin, A., Nies, A. Universality for left-computably enumerable metric spaces. Lobachevskii J Math 35, 292–294 (2014). https://doi.org/10.1134/S1995080214040179
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DOI: https://doi.org/10.1134/S1995080214040179