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Abstract: A fragment of strength and provably recursive functions of n iterated inductive definitions is obtained by restricting second order predicate logic 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 provably recursive functions are also characterized as the fragment of the polymorphic lambda-calculus with the same... (Update)
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BibTeX entry: (Update)
@misc{ aehlig-fragments,
author = "Klaus Aehlig",
title = "On Fragments of Analysis with Strengths of Finitely Iterated Inductive
Definitions",
url = "citeseer.ist.psu.edu/623189.html" }
Citations (may not include all citations):382 Lambda calculi with types - Barendregt - 1992 ACM
106 Lambda calculus notation with nameless dummies (context) - de Bruijn - 1972
43 An inverse of the evaluation functional for typed {calculus (context) - Berger, Schwichtenberg - 1991
12 The type free lambda calculus (context) - Barendregt
10 the computational content of the axiom of choice - Berardi, Bezem et al. - 1998
8 volume 90 of Studies in Logic and the Foundations of Mathema.. (context) - Barwise, of et al. - 1977
7 An introduction to inductive de nitions (context) - Aczel
3 A slow growing analogue to Buchholz' proof (context) - Arai - 1991 DBLP
2 A nitary subsystem of the polymorphic lambda-calculus (context) - Altenkirch, Coquand - 2001
1 undung der intuitionistischen Mathematik III (context) - Brouwer - 1927
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