{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T07:02:14Z","timestamp":1790665334356,"version":"4.1.0"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2013,8,29]],"date-time":"2013-08-29T00:00:00Z","timestamp":1377734400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>A code of the natural numbers is a uniquely-decodable binary code of the\nnatural numbers with non-decreasing codeword lengths, which satisfies Kraft's\ninequality tightly. We define a natural partial order on the set of codes, and\nshow how to construct effectively a code better than a given sequence of codes,\nin a certain precise sense. As an application, we prove that the existence of a\nscale of codes (a well-ordered set of codes which contains a code better than\nany given code) is independent of ZFC.<\/jats:p>","DOI":"10.2168\/lmcs-9(3:7)2013","type":"journal-article","created":{"date-parts":[[2013,11,29]],"date-time":"2013-11-29T13:44:29Z","timestamp":1385732669000},"source":"Crossref","is-referenced-by-count":2,"title":["Universal codes of the natural numbers"],"prefix":"10.46298","volume":"Volume 9, Issue 3","author":[{"given":"Yuval","family":"Filmus","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"25203","published-online":{"date-parts":[[2013,8,29]]},"reference":[{"key":"792:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/975\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/975\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:00:30Z","timestamp":1681243230000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/975"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,29]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-9(3:7)2013","relation":{"is-same-as":[{"id-type":"arxiv","id":"1308.1600","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1308.1600","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8,29]]},"article-number":"975"}}