Totality in applicative theories

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

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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DOI 10.1016/0168-0072(94)00037-4
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References found in this work BETA

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.
The Theory of Functions and Classes. Part I.L. Gordeev - 1988 - Annals of Pure and Applied Logic 38 (1):66.

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Citations of this work BETA

Polynomial Time Operations in Explicit Mathematics.Thomas Strahm - 1997 - Journal of Symbolic Logic 62 (2):575-594.

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