A Simplified Characterisation of Provably Computable Functions of the   System ID_1 of Inductive Definitions
  We present a simplified and streamlined characterisation of provably total computable functions of the theory ID_1 of non-iterated inductive definitions. The idea of the simplification is to employ the method of operator-controlled derivations that was originally introduced by Wilfried Buchholz and afterwards applied by the second author to a characterisation of provably total computable functions of Peano arithmetic PA. 
Naohi Eguchi and Andreas Weiermann
math.LO