Vol. 46, No. 1, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
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