Journal of Symbolic Logic

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

Jeremy Avigad

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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

Zentralblatt MATH identifier
0858.03052

JSTOR
links.jstor.org

Citation

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


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