Talk:Creative and productive sets

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Is it enough to say, creative set is such that it´s complement is productive? IMHO definition lacks a statement saying creative set must be recursively enumarable. See definition at mathworld --Tomash 22:05, 5 January 2006 (UTC)

[edit] The complement of a productive set is not necessarily creative

Creative sets are required by definition to be recursively enumerable (see e.g. these lecture notes by Jean Gallier, but productive sets can be arbitrarily complicated (in particular they do not have to be co-r.e.). As the article stood, it seemed to claim that the set of all true arithmetical statements was co-r.e., which of course is false. --Trovatore 03:00, 22 February 2006 (UTC)