Pure Iteration and Periodicity

A Note on Some Small Sub-recursive Classes
  • Mathias Barra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5028)


We define a hierarchy Open image in new window of small sub-recursive classes, based on the schema of pure iteration. Open image in new window is compared with a similar hierarchy, based on primitive recursion, for which a collapse is equivalent to a collapse of the small Grzegorczyk-classes. Our hierarchy does collapse, and the induced relational class is shown to have a highly periodic structure; indeed a unary predicate is decidable in Open image in new window iff it is definable in Presburger Arithmetic. The concluding discussion contrasts our findings to those of Kutyłowski [12].


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mathias Barra
    • 1
  1. 1.Dept. of MathematicsUniversity of OsloOsloNorway

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