Universal codes of the natural numbers

Yuval Filmus
Logical Methods in Computer Science, Volume 9, Issue 3, 2013, Paper 7

A code of the natural numbers is a uniquely-decodable binary code of the natural numbers with non-decreasing codeword lengths, which satisfies Kraft’s inequality tightly. We define a natural partial order on the set of codes, and show how to construct effectively a code better than a given sequence of codes, in a certain precise sense. As an application, we prove that the existence of a scale of codes (a well-ordered set of codes which contains a code better than any given code) is independent of ZFC.


 author = {Yuval Filmus},
 title = {Universal codes of the natural numbers},
 journal = {Logical Methods in Computer Science},
 volume = {9},
 issue = {3},
 year = {2013},
 pages = {paper 7}
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