Oracle Constructions and Forcing

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


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.


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

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

Personalised recommendations