Journal
JOURNAL OF SYMBOLIC LOGIC
Volume 78, Issue 4, Pages 1055-1085Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.2178/jsl.7804030
Keywords
Computable analysis; metric space theory
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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 L[0, 1] of continuous functions on the unit interval with the supremum metric is not. We also characterize computably categorical subspaces of 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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