Derivation Lengths Classification of Gödel's T Extending Howard's Assignment

@article{Wilken2012DerivationLC,
title={Derivation Lengths Classification of G{\"o}del's T Extending Howard's Assignment},
author={Gunnar Wilken and Andreas Weiermann},
journal={Logical Methods in Computer Science},
year={2012},
volume={8}
}

Let T be Gödel’s system of primitive recursive functionals of finite type in the lambda formulation. We define by constructive means using recursion on nested multisets a multivalued function I from the set of terms of T into the set of natural numbers such that if a term A reduces to a term B and if a natural number I(A) is assigned to A then a natural number I(B) can be assigned to B such that I(A) is greater than I(B). The construction of I is based on Howard’s 1970 ordinal assignment for T… CONTINUE READING