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Intuitionistic Fixed Point Theories for Strictly Positive Operators
Mathematical Logic Quarterly 48 (2):195-202 (2002)
Abstract
In this paper it is shown that the intuitionistic .xed point theory equation image for α times iterated fixed points of strictly positive operator forms is conservative for negative arithmetic and equation image sentences over the theory equation image for α times iterated arithmetic comprehension without set parameters.This generalizes results previously due to Buchholz [5] and Arai [2]My notes
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Citations of this work
A note on predicative ordinal analysis I: Iterated comprehension and transfinite induction.Sato Kentaro - 2019 - Journal of Symbolic Logic 84 (1):226-265.
From hierarchies to well-foundedness.Dandolo Flumini & Kentaro Sato - 2014 - Archive for Mathematical Logic 53 (7-8):855-863.
Quick cut-elimination for strictly positive cuts.Toshiyasu Arai - 2011 - Annals of Pure and Applied Logic 162 (10):807-815.
Intuitionistic fixed point theories over set theories.Toshiyasu Arai - 2015 - Archive for Mathematical Logic 54 (5-6):531-553.
References found in this work
The proof-theoretic analysis of transfinitely iterated fixed point theories.Gerhard JÄger, Reinhard Kahle, Anton Setzer & Thomas Strahm - 1999 - Journal of Symbolic Logic 64 (1):53-67.
On the relationship between ATR 0 and.Jeremy Avigad - 1996 - Journal of Symbolic Logic 61 (3):768-779.
On the relationships between ATR0 and $\widehat{ID}_{.Jeremy Avigad - 1996 - Journal of Symbolic Logic 61 (3):768 - 779.
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.
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