About the proof-theoretic ordinals of weak fixed point theories

Journal of Symbolic Logic 57 (3):1108-1119 (1992)

Abstract

This paper presents several proof-theoretic results concerning weak fixed point theories over second order number theory with arithmetic comprehension and full or restricted induction on the natural numbers. It is also shown that there are natural second order theories which are proof-theoretically equivalent but have different proof-theoretic ordinals

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References found in this work

Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
Elementary Induction on Abstract Structures.Wayne Richter - 1979 - Journal of Symbolic Logic 44 (1):124-125.
Proof Theory and Logical Complexity.Helmut Pfeifer & Jean-Yves Girard - 1989 - Journal of Symbolic Logic 54 (4):1493.

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Citations of this work

Non‐Elementary Speed‐Ups in Logic Calculi.Toshiyasu Arai - 2008 - Mathematical Logic Quarterly 54 (6):629-640.

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