Abstract
Herbrand's Theorem, in the form of\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\exists } \)-inversion lemmata for finitary and infinitary sequent calculi, is the crucial tool for the determination of the provably total function(al)s of a variety of theories. The theories are (second order extensions of) fragments of classical arithmetic; the classes of provably total functions include the elements of the Polynomial Hierarchy, the Grzegorczyk Hierarchy, and the extended Grzegorczyk Hierarchy\(\mathfrak{E}^\alpha \), α < ε0. A subsidiary aim of the paper is to show that the proof theoretic methods used here are distinguished by technical elegance, conceptual clarity, and wide-ranging applicability.
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This paper is dedicated to Kurt Schütte on the occasion of his 80th birthday
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Sieg, W. Herbrand analyses. Arch Math Logic 30, 409–441 (1991). https://doi.org/10.1007/BF01621477
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DOI: https://doi.org/10.1007/BF01621477