Herbrand analyses

Archive for Mathematical Logic 30 (5-6):409-441 (1991)
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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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Wilfried Sieg
Carnegie Mellon University

References found in this work

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