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Symmetric Enumeration Reducibility

  • Charles M. Harris
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)

Abstract

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.

Keywords

Turing Machine Initial Segment Computable Function Jump Operator Enumeration Reducibility 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Charles M. Harris
    • 1
  1. 1.Department of Pure MathematicsUniversity of LeedsLeedsEngland

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