On the Relationships between $ATR0$ And $\widehat{ID}{< \omega}$

Journal of Symbolic Logic 61 (2):768-779 (1996)
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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.

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Jeremy Avigad
Carnegie Mellon University

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