A Simplified Characterisation of Provably Computable Functions of the System ID_1 of Inductive Definitions

TL;DR

This paper simplifies the characterization of provably total computable functions within the ID_1 theory of non-iterated inductive definitions using operator-controlled derivations, building on previous methods applied to Peano arithmetic.

Contribution

It introduces a streamlined method for characterizing provably total functions of ID_1, adapting operator-controlled derivations for this specific theory.

Findings

Simplified characterization of provably total functions of ID_1

Application of operator-controlled derivations to ID_1

Enhanced understanding of the computational strength of ID_1

Abstract

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.