Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 61, Issue 3 (1996), 768-779.
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
Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745075
Mathematical Reviews number (MathSciNet)
MR1412508
Zentralblatt MATH identifier
0858.03052
JSTOR
links.jstor.org
Citation
Avigad, Jeremy. On the Relationships between $ATR_0$ And $\widehat{ID}_{< \omega}$. J. Symbolic Logic 61 (1996), no. 3, 768--779. https://projecteuclid.org/euclid.jsl/1183745075
