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December 2005 Induction and inductive definitions in fragments of second order arithmetic
Klaus Aehlig
J. Symbolic Logic 70(4): 1087-1107 (December 2005). DOI: 10.2178/jsl/1129642116

Abstract

A fragment with the same provably recursive functions as n iterated inductive definitions is obtained by restricting second order arithmetic in the following way. The underlying language allows only up to n+1 nested second order quantifications and those are in such a way, that no second order variable occurs free in the scope of another second order quantifier. The amount of induction on arithmetical formulae only affects the arithmetical consequences of these theories, whereas adding induction for arbitrary formulae increases the strength by one inductive definition.

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Klaus Aehlig. "Induction and inductive definitions in fragments of second order arithmetic." J. Symbolic Logic 70 (4) 1087 - 1107, December 2005. https://doi.org/10.2178/jsl/1129642116

Information

Published: December 2005
First available in Project Euclid: 18 October 2005

zbMATH: 1118.03054
MathSciNet: MR2194238
Digital Object Identifier: 10.2178/jsl/1129642116

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 4 • December 2005
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