The Complexity of Inductive Definability

  • Douglas Cenzer
  • Jeffrey B. Remmel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)


We study the complexity of computable and Σ\(_{\rm 1}^{\rm 0}\) inductive definitions of sets of natural numbers. For we example, we show how to assign natural indices to monotone Σ\(_{\rm 1}^{\rm 0}\)-definitions and we use these to calculate the complexity of the set of all indices of monotone Σ\(_{\rm 1}^{\rm 0}\)-definitions which are computable. We also examine the complexity of new type of inductive definition which we call weakly finitary monotone inductive definitions. Applications are given in proof theory and in logic programming.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Douglas Cenzer
    • 1
  • Jeffrey B. Remmel
    • 2
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

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