## Journal of Symbolic Logic

### On the Relationships between $ATR_0$ And $\widehat{ID}_{< \omega}$

#### Abstract

We show that the theory $ATR_0$ is equivalent to a second-order generalization of the theory $\widehat{ID}_{<\omega}$. As a result, $ATR_0$ is conservative over $\widehat{ID}_{<\omega}$ for arithmetic sentences, though proofs in $ATR_0$ can be much shorter than their $\widehat{ID}_{<\omega}$ counterparts.

#### Article information

Source
J. Symbolic Logic Volume 61, Issue 3 (1996), 768-779.

Dates
First available in Project Euclid: 6 July 2007

Avigad, Jeremy. On the Relationships between $ATR_0$ And $\widehat{ID}_{&lt; \omega}$. J. Symbolic Logic 61 (1996), no. 3, 768--779.https://projecteuclid.org/euclid.jsl/1183745075