Splitting theorems and the jump operator

We investigate the relationship of (jumps of) the degrees of splittings of a computably enumerable set and the degree of the set. We prove that there is a high computably enumerable set whose only proper splittings are low 2.

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Bibliographic Details
Published inAnnals of pure and applied logic Vol. 94; no. 1; pp. 45 - 52
Main Authors Downey, R.G., Shore, Richard A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 05.10.1998
Subjects
Computably enumerable
High
Jump operator
Low 2
Splitting
Computably enumerable
High
03D25
Splitting
Jump operator
Low 2
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Summary:We investigate the relationship of (jumps of) the degrees of splittings of a computably enumerable set and the degree of the set. We prove that there is a high computably enumerable set whose only proper splittings are low 2.
ISSN:0168-0072
DOI:10.1016/S0168-0072(97)00066-3