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Oracle Constructions and Forcing

  • Robert I. Soare
Chapter
Part of the Theory and Applications of Computability book series (THEOAPPLCOM)

Abstract

We have seen in Chapter  5 how Post tried to solve Post's Problem 5.1.1 by defining c.e. sets A with ever thinner complements. Post himself did not live to see the refutation of this approach by [Friedberg 1958], who constructed a maximal set with the thinnest complement of all, and the construction of a complete maximal set by Yates, which refuted Post's approach. Post moved on to understand full Turing reducibility in [Post 1944]. He gave an excellent intuitive description of one set being Turing reducible to another.

Keywords

Minimal Pair Turing Degree Computable Relation Completeness Criterion Turing Reducibility 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Robert I. Soare
    • 1
  1. 1.Department of MathematicsThe University of ChicagoChicagoUSA

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