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The Recursively Enumerable Degrees
Decision problems were the motivating force in the search for a formal definition of algorithm that constituted the beginnings of recursion (computability) theory. In the abstract, given a set A the decision problem for A consist of finding an algorithm which, given input n, decides whether or not n is in A. The classic decision problem for logic is whether a particular sentence is a theorem of...
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We state some general facts on r.e. structures, e.g. we show that the free countable structures in quasivarieties are r.e. and construct acceptable numerations and universal r.e. structures in quasivarieties. The last facts are similar to the existence of acceptable numerations of r.e. sets and creative sets. We state a universality property of the acceptable numerations, classify some index se...
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We say that a real X is relatively r.e. if there exists a real Y such that X is r.e. (Y ) and X 6≤T Y . We say X is relatively REA if there exists such a Y ≤T X. We define A ≤e1 B if there exists a Σ1 set C such that n ∈ A if and only if there is a finite E ⊆ B with (n, E) ∈ C. In this paper we show that a real X is relatively r.e. if and only if X 6≤e1 X. We prove that every nonempty Π01 class...
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For given sets A, B, and Z of natural numbers where the members of Z are z0, z1, . . . in ascending order, one says that A is selected from B by Z if A(i) = B(zi) for all i. Furthermore, say that A is selected from B if A is selected from B by some recursively enumerable set, and that A is selected from B in n steps iff there are sets E0, E1, . . . , En such that E0 = A, En = B, and Ei is selec...
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1978
ISSN: 0003-4843
DOI: 10.1016/0003-4843(78)90027-x