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  1. Exact Bounds for Lengths of Reductions in Typed Λ-Calculus.Arnold Beckmann - 2001 - Journal of Symbolic Logic 66 (3):1277-1285.
    We determine the exact bounds for the length of an arbitrary reduction sequence of a term in the typed λ-calculus with β-, ξ- and η-conversion. There will be two essentially different classifications, one depending on the height and the degree of the term and the other depending on the length and the degree of the term.
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  • An Upper Bound for Reduction Sequences in the Typed Λ-Calculus.Helmut Schwichtenberg - 1991 - Archive for Mathematical Logic 30 (5-6):405-408.
  • How is It That Infinitary Methods Can Be Applied to Finitary Mathematics? Godel's T: A Case Study.Andreas Weiermann - 1998 - Journal of Symbolic Logic 63 (4):1348-1370.
    Inspired by Pohlers' local predicativity approach to Pure Proof Theory and Howard's ordinal analysis of bar recursion of type zero we present a short, technically smooth and constructive strong normalization proof for Godel's system T of primitive recursive functionals of finite types by constructing an $\varepsilon_0$-recursive function [ ]$_0$: T $\rightarrow \omega$ so that a reduces to b implies [a]$_0 > [b]_0$. The construction of [ ]$_0$ is based on a careful analysis of the Howard-Schutte treatment of Godel's T and (...)
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