Intuitionistic Fixed Point Theories for Strictly Positive Operators

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Mathematical Logic Quarterly 48 (2):195-202 (2002)
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Abstract

In this paper it is shown that the intuitionistic fixed 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].

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10.1002/1521-3870(200202)48:2

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Citations of this work

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.

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References found in this work

Reflecting on incompleteness.Solomon Feferman - 1991 - Journal of Symbolic Logic 56 (1):1-49.
On the relationship between ATR 0 and.Jeremy Avigad - 1996 - Journal of Symbolic Logic 61 (3):768-779.
Fixed point theories and dependent choice.Gerhard Jäger & Thomas Strahm - 2000 - Archive for Mathematical Logic 39 (7):493-508.

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