Abstract
We define a hierarchy 
of small sub-recursive classes, based on the schema of pure iteration. 
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 
iff it is definable in Presburger Arithmetic. The concluding discussion contrasts our findings to those of KutyĆowski [12].
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Barra, M. (2008). Pure Iteration and Periodicity. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_5
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DOI: https://doi.org/10.1007/978-3-540-69407-6_5
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