Symmetric Enumeration Reducibility
Symmetric Enumeration reducibility (≤se) is a subrelation of Enumeration reducibility (≤e) in which both the positive and negative information content of sets is compared. In contrast with Turing reducibility (≤T) however, the positive and negative parts of this relation are separate. A basic classification of ≤se in terms of standard reducibilities is carried out and it is shown that the natural embedding of the Turing degrees into the Enumeration degrees easily translates to this context. A generalisation of the relativised Arithmetical Hierarchy is achieved by replacing the relation c.e. in by ≤e and ≤T by ≤se in the underlying framework of the latter.
KeywordsTuring Machine Initial Segment Computable Function Jump Operator Enumeration Reducibility
Unable to display preview. Download preview PDF.