Journal of Symbolic Logic

Computably isometric spaces

Alexander G. Melnikov

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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 $ \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.

Article information

Source
J. Symbolic Logic Volume 78, Issue 4 (2013), 1055-1085.

Dates
First available in Project Euclid: 5 January 2014

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1388953994

Digital Object Identifier
doi:10.2178/jsl.7804030

Mathematical Reviews number (MathSciNet)
MR3156512

Zentralblatt MATH identifier
1332.03008

Keywords
Computable analysis metric space theory

Citation

Melnikov, Alexander G. Computably isometric spaces. J. Symbolic Logic 78 (2013), no. 4, 1055--1085. doi:10.2178/jsl.7804030. http://projecteuclid.org/euclid.jsl/1388953994.


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