## Journal of Symbolic Logic

### Induction and inductive definitions in fragments of second order arithmetic

Klaus Aehlig

#### 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.

#### Article information

Source
J. Symbolic Logic Volume 70, Issue 4 (2005), 1087-1107.

Dates
First available: 18 October 2005

http://projecteuclid.org/euclid.jsl/1129642116

Digital Object Identifier
doi:10.2178/jsl/1129642116

Mathematical Reviews number (MathSciNet)
MR2194238

Zentralblatt MATH identifier
1118.03054

#### Citation

Aehlig, Klaus. Induction and inductive definitions in fragments of second order arithmetic. Journal of Symbolic Logic 70 (2005), no. 4, 1087--1107. doi:10.2178/jsl/1129642116. http://projecteuclid.org/euclid.jsl/1129642116.

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