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

2012
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Logical Methods in Computer Science
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Let T be Goedel'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

doi:10.2168/lmcs-8(1:19)2012
fatcat:vdthzsigprffrkk6dvlowejdza