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Computably Isometric Spaces

Published online by Cambridge University Press:  12 March 2014

Alexander G. Melnikov
Alexander G. Melnikov*
Affiliation:
School of Mathematics, Statistics, and Operations Research, Victoria University of Wellington, Wellington, New Zealand, E-mail: alexander.g.melnikov@gmail.com
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Abstract

We say that an uncountable metric space is computably categorical if every two computable structures on this space are equivalent up to a computable isometry. We show that Cantor space, the Urysohn space, and every separable Hilbert space are computably categorical, but the space [0, 1] of continuous functions on the unit interval with the supremum metric is not. We also characterize computably categorical subspaces of ℝn, and give a sufficient condition for a space to be computably categorical. Our interest is motivated by classical and recent results in computable (countable) model theory and computable analysis.

Keywords

Computable analysismetric space theory
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 4 , December 2013 , pp. 1055 - 1085
Copyright
Copyright © Association for Symbolic Logic 2013

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