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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 ordinalsLinks
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Citations of this work
Some results on cut-elimination, provable well-orderings, induction and reflection.Toshiyasu Arai - 1998 - Annals of Pure and Applied Logic 95 (1-3):93-184.
Second order theories with ordinals and elementary comprehension.Gerhard Jäger & Thomas Strahm - 1995 - Archive for Mathematical Logic 34 (6):345-375.
Non‐elementary speed‐ups in logic calculi.Toshiyasu Arai - 2008 - Mathematical Logic Quarterly 54 (6):629-640.
References found in this work
Proof Theory and Logical Complexity.Helmut Pfeifer & Jean-Yves Girard - 1989 - Journal of Symbolic Logic 54 (4):1493.
Elementary Induction on Abstract Structures.Wayne Richter - 1979 - Journal of Symbolic Logic 44 (1):124-125.
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