Inductive definitions over a predicative arithmetic

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Annals of Pure and Applied Logic 136 (1-2):175-188 (2005)
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Abstract

Girard’s maxim, that Peano Arithmetic is a theory of one inductive definition, is re-examined in the light of a weak theory EA formalising basic principles of Nelson’s predicative Arithmetic

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10.1016/j.apal.2005.05.011

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References found in this work

[product]¹2-logic, Part 1: Dilators.Jean-Yves Girard - 1981 - Annals of Mathematical Logic 21 (2):75.
Π12-logic, Part 1: Dilators.Jean-Yves Girard - 1981 - Annals of Mathematical Logic 21 (2-3):75-219.
A slow growing analogue to buchholz' proof.Toshiyasu Arai - 1991 - Annals of Pure and Applied Logic 54 (2):101-120.
An independence result for (II11-CA)+BI.Wilfried Buchholz - 1987 - Annals of Pure and Applied Logic 33 (C):131-155.
Consistency proof via pointwise induction.Toshiyasu Arai - 1998 - Archive for Mathematical Logic 37 (3):149-165.

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