Totality in applicative theories

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Annals of Pure and Applied Logic 74 (2):105-120 (1995)
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Abstract

In this paper we study applicative theories of operations and numbers with the non-constructive minimum operator in the context of a total application operation. We determine the proof-theoretic strength of such theories by relating them to well-known systems like Peano Arithmetic PA and the system <0 of second order arithmetic. Essential use will be made of so-called fixed-point theories with ordinals, certain infinitary term models and Church-Rosser properties

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10.1016/0168-0072(94)00037-4

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Citations of this work

Truth in applicative theories.Reinhard Kahle - 2001 - Studia Logica 68 (1):103-128.
Polynomial time operations in explicit mathematics.Thomas Strahm - 1997 - Journal of Symbolic Logic 62 (2):575-594.

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References found in this work

Fixed points in Peano arithmetic with ordinals.Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 60 (2):119-132.
Proof-theoretical analysis: weak systems of functions and classes.L. Gordeev - 1988 - Annals of Pure and Applied Logic 38 (1):1-121.

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