Non-Generable RE Sets
نویسنده
چکیده
Let E be a finite alphabet and let W be the set of words on Z. A subset A of W is said to be generable if it is the closure of a computable inductive operator F over W; if F is monotone, then A is monotone generable. (The basic facts about inductive operators and about RE sets needed in this paper will be given in section one.) Now any generable set is RE and any RE set is I-i reducible to a (monotone) generable set. The question naturally arises whether all RE sets are actually generable. One purpose of this paper is to answer that question in the negative.
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