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December 2013 Computably isometric spaces
Alexander G. Melnikov
J. Symbolic Logic 78(4): 1055-1085 (December 2013). DOI: 10.2178/jsl.7804030

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 $ \mathcal{C}[0,1]$ of continuous functions on the unit interval with the supremum metric is not. We also characterize computably categorical subspaces of $\mathbb{R}^n$, 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.

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Alexander G. Melnikov. "Computably isometric spaces." J. Symbolic Logic 78 (4) 1055 - 1085, December 2013. https://doi.org/10.2178/jsl.7804030

Information

Published: December 2013
First available in Project Euclid: 5 January 2014

zbMATH: 1332.03008
MathSciNet: MR3156512
Digital Object Identifier: 10.2178/jsl.7804030

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 4 • December 2013
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