Vol. 46, No. 1, 1973

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The class of recursively enumerable subsets of a recursively enumerable set

Louise Hay

Vol. 46 (1973), No. 1, 167–183

For any set α, let 𝜃Aα denote the index set of the class of all recursively enumerable (r.e.) subsets of α (i.e., if {Wx}x0 is a standard enumeration of all r.e. sets, 𝜃Aα = {x|Wx α}.) The purpose of this paper is to examine the possible Turing degrees of the sets 𝜃Aα when α is r.e. It is proved that if b is any nonrecursive r.e. degree, the Turing degrees of sets 𝜃Aα for α r.e., α b, are exactly the degrees c > 0such that c is r.e. in b.

Mathematical Subject Classification
Primary: 02F25
Received: 2 January 1972
Published: 1 May 1973
Louise Hay