Journal of Symbolic Logic 70 (4):1087 - 1107 (2005)
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
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
A Slow Growing Analogue to Buchholz' Proof.Toshiyasu Arai - 1991 - Annals of Pure and Applied Logic 54 (2):101-120.
Citations of this work BETA
Parameter-Free Polymorphic Types.Klaus Aehlig - 2008 - Annals of Pure and Applied Logic 156 (1):3-12.
Similar books and articles
Tracking Track Records, I.Peter Lipton - 2000 - Aristotelian Society Supplementary Volume 74 (1):179–205.
First Order Theories for Nonmonotone Inductive Definitions: Recursively Inaccessible and Mahlo.Gerhard Jäger - 2001 - Journal of Symbolic Logic 66 (3):1073-1089.
On the Strength of König's Duality Theorem for Countable Bipartite Graphs.Stephen G. Simpson - 1994 - Journal of Symbolic Logic 59 (1):113-123.
There Are No Universal Rules for Induction.John D. Norton - 2010 - Philosophy of Science 77 (5):765-777.
Nonstandard Arithmetic and Reverse Mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
Finite Injury and ∑1-Induction.Michael Mytilinaios - 1989 - Journal of Symbolic Logic 54 (1):38 - 49.
Quantum Mathematics.J. Michael Dunn - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Functional Interpretation and Inductive Definitions.Jeremy Avigad & Henry Towsner - 2009 - Journal of Symbolic Logic 74 (4):1100-1120.
The Role of Parameters in Bar Rule and Bar Induction.Michael Rathjen - 1991 - Journal of Symbolic Logic 56 (2):715-730.
A Material Dissolution of the Problem of Induction.John D. Norton - 2013 - Synthese 191 (4):1-20.
Added to index2010-08-24
Total downloads21 ( #235,740 of 2,164,535 )
Recent downloads (6 months)3 ( #128,957 of 2,164,535 )
How can I increase my downloads?