Classiication: Mathematics
نویسنده
چکیده
A set A of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. The class of sets B which contain the same information as A under Turing computability ( T) is the (Turing) degree of A, and a degree is c.e. if it contains an c.e. set. The extension of embedding problem for the c.e. degrees R = (R; <;0;00) asks given nite partially ordered sets P Q with least and greatest elements, whether every embedding of P into R can be extended to an embedding of Q into R. Many of the most signi cant theorems giving an algebraic insight into R have asserted either extension or nonextension of embeddings. We extend and unify these results and their proofs to produce complete and complementary criteria and techniques to analyze instances of extension and nonextension. We conclude that the full extension of embedding problem is decidable. 2
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