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A reducibility related to being hyperimmune-free.
- Source :
-
Annals of Pure & Applied Logic . Jul2014, Vol. 165 Issue 7/8, p1291-1300. 10p. - Publication Year :
- 2014
-
Abstract
- Abstract: The main topic of the present work is the relation that a set X is strongly hyperimmune-free relative to Y. Here X is strongly hyperimmune-free relative to Y if and only if for every partial X-recursive function p there is a partial Y-recursive function q such that every a in the domain of p is also in the domain of q and satisfies , that is, p is majorised by q. For X being hyperimmune-free relative to Y, one also says that X is pmaj-reducible to Y . It is shown that between degrees not above the Halting problem the pmaj-reducibility coincides with the Turing reducibility and that therefore only recursive sets have a strongly hyperimmune-free Turing degree while those sets Turing above the Halting problem bound uncountably many sets with respect to the pmaj-relation. So pmaj-reduction is identical with Turing reduction on a class of sets of measure 1. Moreover, every pmaj-degree coincides with the corresponding Turing degree. The pmaj-degree of the Halting problem is definable with the pmaj-relation. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01680072
- Volume :
- 165
- Issue :
- 7/8
- Database :
- Academic Search Index
- Journal :
- Annals of Pure & Applied Logic
- Publication Type :
- Academic Journal
- Accession number :
- 96020392
- Full Text :
- https://doi.org/10.1016/j.apal.2014.04.002