Turing Reducibility

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


After his epochal paper in 1936 on Turing machines, Turing wrote a Ph.D. dissertation with Alonzo Church which was published in 1939. A tiny part of this paper in section 4 contained the germ of one of the most important ideas in all of modern computability theory. In half a page Turing suggested augmenting his formera-machines by adding some kind of “oracle” which could supply the answers to specific questions during the computation.


Computable Function Computable Sequence Turing Degree Cantor Space Turing Reducibility 
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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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