{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T03:13:14Z","timestamp":1788923594381,"version":"build-2803163510"},"reference-count":38,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":101,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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 <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120012643X_inline1\"\/>[0, 1] of continuous functions on the unit interval with the supremum metric is not. We also characterize computably categorical subspaces of \u211d<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup>, 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.<\/jats:p>","DOI":"10.2178\/jsl.7804030","type":"journal-article","created":{"date-parts":[[2014,1,5]],"date-time":"2014-01-05T20:33:25Z","timestamp":1388954005000},"page":"1055-1085","source":"Crossref","is-referenced-by-count":35,"title":["Computably Isometric Spaces"],"prefix":"10.1017","volume":"78","author":[{"given":"Alexander G.","family":"Melnikov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120012643X_ref037","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56999-9"},{"key":"S002248120012643X_ref033","first-page":"230","article-title":"On Computable Numbers, with an Application to the Entscheidungsproblem","volume":"42","author":"Turing","year":"1936","journal-title":"Proceedings of the London Mathematical Society"},{"key":"S002248120012643X_ref027","first-page":"30","volume-title":"Proceedings of the International Congress of Mathematicians. 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