## Journal of Symbolic Logic

### Some Theories with Positive Induction of Ordinal Strength $\varphi\omega 0$

#### Abstract

This paper deals with: (i) the theory $\mathrm{ID}^{\tt\#}_1$ which results from $\widehat{\mathrm{ID}}_1$ by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory $\mathrm{BON}(\mu)$ plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are $\Sigma$ in the ordinals. We show that these systems have proof-theoretic strength $\varphi\omega 0$.

#### Article information

Source
J. Symbolic Logic, Volume 61, Issue 3 (1996), 818-842.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745079

Mathematical Reviews number (MathSciNet)
MR1412512

Zentralblatt MATH identifier
0862.03031

JSTOR
Jager, Gerhard; Strahm, Thomas. Some Theories with Positive Induction of Ordinal Strength $\varphi\omega 0$. J. Symbolic Logic 61 (1996), no. 3, 818--842. https://projecteuclid.org/euclid.jsl/1183745079